A061687 Generalized Bell numbers: column 6 of A275043.

1, 1, 33, 8506, 9483041, 33056715626, 293327384637282, 5747475089121405893, 224054040415856117594913, 16044797009828490454609378642, 1981736776623437001042672440089658, 401147408702290404750740714717055504773, 127573929384655691416638350563783440408133922

Offset: 0

Author

N. J. A. Sloane, Jun 18 2001

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..117
• J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, Extended Bell and Stirling Numbers From Hypergeometric Exponentiation, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

Crossrefs

Column k=6 of A275043.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n, k)^6*(n-k)*a(k)/n, k=0..n-1))
    end:
seq(a(n), n=0..15); # Alois P. Heinz, Nov 07 2008

Mathematica

a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n, k]^6*(n-k)*a[k]/n, {k, 0, n-1}]]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 19 2014, after Alois P. Heinz *)

Formula

Sum_{n>=0} a(n) * x^n / (n!)^6 = exp(Sum_{n>=1} x^n / (n!)^6). - Ilya Gutkovskiy, Jul 17 2020

Extensions

More terms from Alois P. Heinz, Nov 07 2008