Sums of odd powers
Pk(n) = 1k + 3k + 5k + . . . + (2n-1)k
Exponent
(k)		 Sum (Pk(n)) Shortening with U=4n2-1
1n2------------------------------------
2n(4n2-1)/3nU/3
3n2(2n2-1)------------------------------------
4n(3(4n2-1)2-4(4n2-1))/15 nU(3U-4)/15
5n2(16n4-20n2+7)/3 ------------------------------------
6n(3(4n2-1)3-12(4n2-1)2+16(4n2-1))/21 nU(3U2-12U+16)/21
7n2(48n6-112n4+98n2-31)/3 ------------------------------------
Exponent
(k)		Sum (Pk(n))
8nU(5U3-40U2+144U-192)/45
9n2(768n8-2880n6+4704n4-3720n2+1143)/15
10nU(3U4-40U3+272U2-960U+1280)/33
11n2(512n10-2816n8+7392n6-10912n4+8382n2-2555)/3
12nU(105U5-2100U4+22960U3-151040U2+530688U-707584)/1365
13n2(61440n12-465920n10+1793792n8-4255680n6+6102096n4-4650100n2+1414477)/105
14nU(3U6-84U5+1344U4-14080U3+91904U2-322560U+430080)/45
15n2(6144n14-61440n12+326144n10-1134848n8+2615184n6-3720080n4+2828954n2-860055)/3
16nU(15U7-560U6+12320U5-187520U4+1944320U3-12666880U2+44445696U-59260928)/255
17n2(327680n16-4177920n14+29245440n12-140308480n10+474220032n8-1084137600n6+1538950976n4-1169674800n2+355554717)/45
18nU(105U8-5040U7+145824U6-3034752U5+45626112U4-471869440U3+3072684032U2-10780753920U+14374338560)/1995
19n2(2752512n18-43581440n16+388964352n14-2460794880n12+11467502592n10-38450746880n8+87720205632n6-124453398720n4+94577554722n2-28748457785)/105
20nU(165U9-9900U8+364320U7-9926400U6+203723520U5-3053460480U4+31559004160U3-205479280640U2+720928309248U-961237745664)/3465
21n2(15728640n20-302776320n18+3355770880n16-27068743680n14+166341795840n12-769014937600n10+2573126031872n8-5867088796800n6+8322824815536n4-6324660712700n2+1922471824497)/165
22nU(15U10-1100U9+50160U8-1731840U7+46472448U6-950426624U5+14234230784U4-147094241280U3+957695852544U2-3360081838080U+4480109117440)/345
23n2(15728640n22-361758720n20+4874698752n18-48829890560n16+382586130432n14-2332396953600n12+10760345224192n10-35984811287040n8+82039273181712n6-116373757113680n4+88433703926862n2-26880641886945)/45
24-30(In the author's form and without supervision)
CLICK HERE

Authors:
Gerzson Keri
keri@oplab.sztaki.hu
(*-15)		 Barbara Keri
kerib@ludens.elte.hu
(16-17)		 Jozsef Ureczky
http://www.angelfire.com/id/ureczky/
(18-23)
Gabor Zavarko
zavarko@matavnet.hu
(24-30)

Tables: Initial Page

Copyright © 1997 Gerzson Kéri