A292318 Expansion of Product_{k>=1} ((1 + k!*x^k)/(1 - k!*x^k)).

1, 2, 6, 22, 90, 434, 2442, 15874, 118722, 1009586, 9640866, 102243682, 1191949122, 15141785570, 208068223458, 3073613823778, 48554040330210, 816547584905186, 14562214993474914, 274463503469613538, 5450631032885614050, 113749623991878727394

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

Convolution of A077365 and A265950.

a(n) ~ 2 * n! * (1 + 2/n + 6/n^2 + 28/n^3 + 162/n^4 + 1134/n^5 + 9368/n^6 + 89502/n^7 + 974338/n^8 + 11948360/n^9 + 163462518/n^10). - Vaclav Kotesovec, Sep 15 2017

Mathematica

nmax = 25; CoefficientList[Series[Product[(1 + k!*x^k)/(1 - k!*x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Sep 15 2017 *)

Crossrefs

Cf. A077365, A265950, A292319.

Sequence in context: A264601 A308564 A226435 * A150271 A150272 A342289

Adjacent sequences: A292315 A292316 A292317 * A292319 A292320 A292321

Keyword

nonn

Author

Seiichi Manyama, Sep 14 2017

Status

approved