A284898 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A284898

Expansion of Product_{k>=1} 1/(1+x^k)^(k^4) in powers of x.

1, -1, -15, -66, -54, 725, 4580, 12739, 3346, -149076, -791226, -2182124, -1656973, 16553206, 100646954, 318795473, 506196578, -818806580, -9148048880, -36415709566, -87180585636, -70923559814, 484810027389, 2992082912770, 9866919438716, 19936695359140

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..3995

FORMULA

a(0) = 1, a(n) = -(1/n)*Sum_{k=1..n} A284926(k)*a(n-k) for n > 0. - Seiichi Manyama, Apr 06 2017

MATHEMATICA

CoefficientList[Series[Product[1/(1 + x^k)^(k^4) , {k, 40}], {x, 0, 40}], x] (* Indranil Ghosh, Apr 05 2017 *)

PROG

(PARI) x= 'x + O('x^40); Vec(prod(k=1, 40, 1/(1 + x^k)^(k^4))) \\ Indranil Ghosh, Apr 05 2017

CROSSREFS

Cf. A248883.

Product_{k>=1} 1/(1+x^k)^(k^m): A081362 (m=0), A255528 (m=1), A284896 (m=2), A284897 (m=3), this sequence (m=4), A284899 (m=5).

Sequence in context: A090026 A027526 A334802 * A033653 A088058 A062392

Adjacent sequences: A284895 A284896 A284897 * A284899 A284900 A284901

KEYWORD

sign

AUTHOR

Seiichi Manyama, Apr 05 2017

STATUS

approved