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A002309 Sum of fourth powers of odd numbers.
(Formerly M5359 N2327)
+0
2
1, 82, 707, 3108, 9669, 24310, 52871, 103496, 187017, 317338, 511819, 791660, 1182285, 1713726, 2421007, 3344528, 4530449, 6031074, 7905235, 10218676, 13044437, 16463238, 20563863, 25443544, 31208345, 37973546, 45864027, 55014652, 65570653, 77688014 (list; graph; listen)
OFFSET

1,2

REFERENCES

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359.

F. E. Croxton and D. J. Cowden, Applied General Statistics. 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1955, p. 742.

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

FORMULA

a(n)=(48*n^5-40*n^3+7*n)/15. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 29 2003

MAPLE

A002309:=(1+76*z+230*z**2+76*z**3+z**4)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]

MATHEMATICA

Table[(48*n^5 - 40*n^3 + 7*n)/15, {n, 0, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006

CROSSREFS

Cf. A002593.

Sequence in context: A005972 A082972 A031422 this_sequence A128959 A083386 A093282

Adjacent sequences: A002306 A002307 A002308 this_sequence A002310 A002311 A002312

KEYWORD

nonn,nice

AUTHOR

njas

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Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


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