A061688 - OEIS

%I #25 Jan 17 2025 11:18:13

%S 1,1,65,48844,209175233,3464129078126,173566857025139312,

%T 22208366234650578141209,6409515697874502425444186817,

%U 3794729706423816704068204814925754,4276126299841623727960390049367617509190,8631647765438316626054238101611711249984175399

%N Generalized Bell numbers: column 7 of A275043.

%H Alois P. Heinz, <a href="/A061688/b061688.txt">Table of n, a(n) for n = 0..100</a>

%H J.-M. Sixdeniers, K. A. Penson and A. I. Solomon, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/SIXDENIERS/bell.html">Extended Bell and Stirling Numbers From Hypergeometric Exponentiation</a>, J. Integer Seqs. Vol. 4 (2001), #01.1.4.

%F Sum_{n>=0} a(n) * x^n / (n!)^7 = exp(Sum_{n>=1} x^n / (n!)^7). - _Ilya Gutkovskiy_, Jul 17 2020

%p a:= proc(n) option remember; `if`(n=0, 1,

%p       add(binomial(n, k)^7*(n-k)*a(k)/n, k=0..n-1))

%p     end:

%p seq(a(n), n=0..12);  # _Alois P. Heinz_, Nov 07 2008

%t a[n_] := a[n] = If[n == 0, 1, Sum[Binomial[n, k]^7*(n-k)*a[k]/n, {k, 0, n-1}]]; Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, Apr 17 2014, after _Alois P. Heinz_ *)

%Y Column k=7 of A275043.

%K nonn,changed

%O 0,3

%A _N. J. A. Sloane_, Jun 18 2001

%E More terms from _Alois P. Heinz_, Nov 07 2008