A294462 E.g.f.: Product_{k>0} (1-k*x^k)^(-1/k).

1, 1, 4, 18, 132, 900, 10080, 93240, 1285200, 16526160, 264600000, 3950100000, 81280584000, 1401728328000, 30861115084800, 663835444272000, 16425316331424000, 380082583808928000, 10885891543502976000, 279441709690118976000, 8697410321979899520000

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..424

Formula

a(0) = 1 and a(n) = (n-1)! * Sum_{k=1..n} A055225(k)*a(n-k)/(n-k)! for n > 0.

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} j^(k-1)*x^(j*k)/k). - Ilya Gutkovskiy, May 28 2018

Prog

(PARI) N=66; x='x+O('x^N); Vec(serlaplace(1/prod(k=1, N, (1-k*x^k)^(1/k))))

Crossrefs

Column k=1 of A294761.

Cf. A028342, A055225, A294463.

Sequence in context: A158341 A144272 A034517 * A194559 A356542 A371038

Adjacent sequences: A294459 A294460 A294461 * A294463 A294464 A294465

Keyword

nonn

Author

Seiichi Manyama, Oct 31 2017

Status

approved