A316084 Product_{k>=1} 1/(1 - a(k)*x^k) = Sum_{k>=0} k!*x^k.

1, 1, 4, 17, 92, 566, 4156, 34023, 314348, 3195658, 35703996, 433259908, 5687955724, 80248240822, 1211781628060, 19496367748659, 333041104402860, 6019720779293770, 114794574818830716, 2303327555284622304, 48509766568956367372, 1069982619999485015070

Offset

1,3

Links

Seiichi Manyama, Table of n, a(n) for n = 1..449

Formula

a(n) ~ n! * (1 - 1/n - 1/n^2 - 4/n^3 - 23/n^4 - 171/n^5 - 1542/n^6 - 16241/n^7 - 194973/n^8 - 2622610/n^9 - 39027573/n^10 - ...), for coefficients see A113869. - Vaclav Kotesovec, Jun 18 2019

a(2*n-1) = A158094(2*n-1). - Vaclav Kotesovec, Jun 18 2019

Example

1/((1-x)*(1-x^2)*(1-4*x^3)*(1-17*x^4)* ... ) = 1 + x + 2*x^2 + 6*x^3 + 24*x^4 + ... .

Crossrefs

Cf. A000142, A113869, A158094.

Sequence in context: A141154 A347340 A355295 * A112354 A020011 A239914

Adjacent sequences: A316081 A316082 A316083 * A316085 A316086 A316087

Keyword

nonn

Author

Seiichi Manyama, Jun 23 2018

Status

approved