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A299164 Expansion of 1/(1 - x*Product_{k>=1} (1 + k*x^k)). 10
1, 1, 2, 5, 14, 35, 91, 233, 597, 1517, 3885, 9922, 25333, 64683, 165181, 421828, 1077277, 2750993, 7025168, 17940298, 45814165, 116996152, 298774246, 762982615, 1948434235, 4975732669, 12706571546, 32448880807, 82864981016, 211613009498, 540397935771, 1380018797044, 3524165721799 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/(1 - x*Product_{k>=1} (1 + k*x^k)).

a(0) = 1; a(n) = Sum_{k=1..n} A022629(k-1)*a(n-k).

MATHEMATICA

nmax = 32; CoefficientList[Series[1/(1 - x Product[1 + k x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Antidiagonal sums of A297321.

Cf. A022629, A067687, A299105, A299106, A299108, A299162, A299166, A299167.

Sequence in context: A018015 A080039 A265226 * A131408 A137917 A244099

Adjacent sequences:  A299161 A299162 A299163 * A299165 A299166 A299167

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 04 2018

STATUS

approved

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Last modified May 27 13:51 EDT 2018. Contains 304694 sequences. (Running on oeis4.)