A346454 - OEIS

A346454

a(n) = [x^n] Product_{k>=1} (1 + n^(k+1)*x^k) / (1 - n^(k+1)*x^k).

1, 2, 48, 2592, 223232, 31125000, 6446926080, 1892514990688, 749710432272384, 385769883231774522, 249932498200000000000, 198950665850610546765024, 190770235699567102280073216, 216806274426828873068796386600, 288094786833316639387122903613440

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) ~ 2 * n^(2*n).

MATHEMATICA

Table[SeriesCoefficient[Product[(1 + n^(k + 1)*x^k)/(1 - n^(k + 1)*x^k), {k, 1, n}], {x, 0, n}], {n, 0, 20}]

Table[SeriesCoefficient[2*x + ((1 - n)*QPochhammer[-n, n*x, 1 + n]) / ((1 + n)*QPochhammer[n, n*x, 1 + n]), {x, 0, n}], {n, 0, 20}]

CROSSREFS

Cf. A344094, A344095, A346452.

Sequence in context: A114714 A186416 A210723 * A322750 A367537 A346019

Adjacent sequences: A346451 A346452 A346453 * A346455 A346456 A346457

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jul 19 2021

STATUS

approved