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A301518 a(n) = [x^n] Product_{k>=1} (1 + x^(k^2))^n. 2
1, 1, 1, 1, 5, 26, 91, 246, 589, 1468, 4226, 13311, 41471, 122864, 351184, 1001876, 2920957, 8698612, 26070130, 77707056, 229959130, 679050870, 2011457295, 5986185690, 17866178695, 53343031301, 159149943668, 474683353849, 1416730630936, 4233405443596 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

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

FORMULA

a(n) ~ c * d^n / sqrt(n), where d = 3.04074590736461391963643911... and c = 0.2268848664201836146769277...

MATHEMATICA

Table[SeriesCoefficient[Product[(1 + x^(k^2))^n, {k, 1, n}], {x, 0, n}], {n, 0, 30}]

CROSSREFS

Cf. A033461, A281790, A291649, A300974.

Sequence in context: A210367 A261347 A079909 * A047669 A297689 A002316

Adjacent sequences:  A301515 A301516 A301517 * A301519 A301520 A301521

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Mar 23 2018

STATUS

approved

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Last modified March 26 14:18 EDT 2019. Contains 321497 sequences. (Running on oeis4.)