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A305655 a(n) = [x^n] exp(Sum_{k>=1} (-1)^(k+1)*x^k*(1 + x^k)/(k*(1 - x^k)^n)). 1
1, 1, 3, 13, 54, 290, 1674, 10857, 76398, 580230, 4706734, 40598349, 370694845, 3569027696, 36100349833, 382360758863, 4228730647420, 48716663849192, 583403253712747, 7248883337962522, 93291181556742684, 1241632098163126324, 17064777292709034968, 241874821482784132204 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..23.

N. J. A. Sloane, Transforms

FORMULA

a(n) = [x^n] Product_{k>=1} (1 + x^k)^(2*binomial(n+k-2,n-1)-binomial(n+k-3,n-2)).

MATHEMATICA

Table[SeriesCoefficient[Exp[Sum[(-1)^(k + 1) x^k (1 + x^k)/(k (1 - x^k)^n), {k, 1, n}]], {x, 0, n}], {n, 0, 23}]

Table[SeriesCoefficient[Product[(1 + x^k)^(2 Binomial[n + k - 2, n - 1] - Binomial[n + k - 3, n - 2]), {k, 1, n}], {x, 0, n}], {n, 0, 23}]

CROSSREFS

Cf. A027998, A255835, A281156, A293554, A305206, A305654.

Sequence in context: A048514 A037779 A323264 * A308349 A140320 A037583

Adjacent sequences:  A305652 A305653 A305654 * A305656 A305657 A305658

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jun 07 2018

STATUS

approved

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Last modified November 17 13:12 EST 2019. Contains 329230 sequences. (Running on oeis4.)