A076900 Expansion of e.g.f.: 1/Product_{m>0} (1-x^m/(m-1)!).

1, 1, 4, 15, 88, 505, 4056, 31549, 311816, 3083049, 36343720, 431215741, 5937234348, 82236865165, 1291252453050, 20477737537755, 361495828272496, 6449450737736065, 126566562342343176, 2509520619696338269, 54179963857121953460, 1182248224137860933781

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..450

Formula

E.g.f.: exp(Sum_{k>=1} Sum_{j>=1} x^(j*k)/(k*((j - 1)!)^k)). - Ilya Gutkovskiy, Sep 13 2018

a(n) ~ c * n * n!, where c = A247551/2. - Vaclav Kotesovec, Sep 13 2018

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(n, i)*i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);  # Alois P. Heinz, May 11 2016

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i-1] + If[i > n, 0, b[n-i, i] Binomial[n, i] i]]];
a[n_] := b[n, n];
a /@ Range[0, 30] (* Jean-François Alcover, Nov 03 2020, after Alois P. Heinz *)

Crossrefs

Cf. A005651, A032299.

Sequence in context: A079155 A306178 A304920 * A346941 A081011 A008829

Adjacent sequences: A076897 A076898 A076899 * A076901 A076902 A076903

Keyword

nonn

Author

Vladeta Jovovic, Nov 26 2002

Status

approved