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A258341 Expansion of Product_{k>=1} (1+x^k)^(k*(k+1)). 9
1, 2, 7, 24, 65, 184, 487, 1254, 3145, 7706, 18480, 43490, 100692, 229472, 515802, 1144416, 2508948, 5439642, 11671859, 24801738, 52221911, 109013538, 225718717, 463769652, 945915199, 1915895576, 3854803572, 7706786958, 15314564282, 30255672820, 59440488874 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

FORMULA

a(n) ~ 7^(1/8) / (2^(47/24) * 15^(1/8) * n^(5/8)) * exp(2025*Zeta(3)^3 / (49*Pi^8) - 135*(15/14)^(1/4) * Zeta(3)^2 / (14*Pi^5) * n^(1/4) + 3*sqrt(15/14) * Zeta(3) / Pi^2 * sqrt(n) + 2*(14/15)^(1/4)*Pi/3 * n^(3/4)), where Zeta(3) = A002117.

MATHEMATICA

nmax=30; CoefficientList[Series[Product[(1+x^k)^(k*(k+1)), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A027998, A028377, A027999, A258342, A258343, A258344, A258345, A258346, A258347.

Sequence in context: A112089 A075062 A022497 * A054128 A082047 A341803

Adjacent sequences:  A258338 A258339 A258340 * A258342 A258343 A258344

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, May 27 2015

STATUS

approved

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Last modified August 8 10:04 EDT 2022. Contains 356009 sequences. (Running on oeis4.)