A074708 -log(1-Sum_{n>0} x^n/n^2) = Sum_{n>=0} a(n)*x^n/n!^2.

1, 3, 25, 406, 10856, 432536, 24032380, 1776015088, 168482342208, 19958023887552, 2887514448643584, 501074299946343168, 102727197888801668352, 24564844379606631001344, 6776711942017520895558912, 2136315270266212479331055616, 763191034622566084583650197504

Offset: 1

Author

Vladeta Jovovic, Sep 04 2002

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A003713.

Programs

Mathematica

nmax = 20; Rest[CoefficientList[Series[-Log[1 - Sum[x^k/k^2, {k, 1, nmax}]], {x, 0, nmax}], x] * Range[0, nmax]!^2] (* Vaclav Kotesovec, Jul 17 2021 *)

PARI

seq(n)={Vec(serlaplace(serlaplace(-log(O(x*x^n) + 1 - sum(k=1, n, x^k/k^2)))))} \\ Andrew Howroyd, Jan 27 2020

Formula

a(n) = ((n-1)!)^2 + (1/n) * Sum_{k=1..n-1} (binomial(n,k) * (k-1)!)^2 * (n-k) * a(n-k). - Ilya Gutkovskiy, Jul 16 2021

a(n) ~ d^n * n! * (n-1)!, where d = 1.31312358308891164912353600222812555333413518214112353115268393... - Vaclav Kotesovec, Jul 17 2021

Extensions

Terms a(15) and beyond from Andrew Howroyd, Jan 27 2020