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A061687 Generalized Bell numbers: column 6 of A275043.

%I A061687 #31 Jan 17 2025 11:19:38
%S A061687 1,1,33,8506,9483041,33056715626,293327384637282,5747475089121405893,
%T A061687 224054040415856117594913,16044797009828490454609378642,
%U A061687 1981736776623437001042672440089658,401147408702290404750740714717055504773,127573929384655691416638350563783440408133922
%N A061687 Generalized Bell numbers: column 6 of A275043.
%H A061687 Alois P. Heinz, <a href="/A061687/b061687.txt">Table of n, a(n) for n = 0..117</a>
%H A061687 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 A061687 Sum_{n>=0} a(n) * x^n / (n!)^6 = exp(Sum_{n>=1} x^n / (n!)^6). - _Ilya Gutkovskiy_, Jul 17 2020
%p A061687 a:= proc(n) option remember; `if`(n=0, 1,
%p A061687       add(binomial(n, k)^6*(n-k)*a(k)/n, k=0..n-1))
%p A061687     end:
%p A061687 seq(a(n), n=0..15); # _Alois P. Heinz_, Nov 07 2008
%t A061687 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_ *)
%Y A061687 Column k=6 of A275043.
%K A061687 nonn
%O A061687 0,3
%A A061687 _N. J. A. Sloane_, Jun 18 2001
%E A061687 More terms from _Alois P. Heinz_, Nov 07 2008