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A061684 Generalized Bell numbers. 5
1, 1, 5, 64, 1613, 69026, 4566992, 437665649, 57903766797, 10193400044254, 2319001344297830, 665816738235745559, 236563125351122920088, 102303284135845463907107, 53093636013475924370369829, 32666276100771741793923209939, 23573762287735885858839134983437 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..215

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.

FORMULA

G.f.: Sum_{n>=0} a(n)*x^n/n!^3 = exp( Sum_{n>=1} x^n/n!^3 ). [Paul D. Hanna, Mar 15 2012]

MAPLE

b:= proc(n) option remember; `if`(n=0, 1,

      add(b(n-i)*binomial(n-1, i-1)/i!^2, i=1..n))

    end:

a:= n-> b(n)*n!^2:

seq(a(n), n=0..20);  # Alois P. Heinz, May 11 2016

MATHEMATICA

b[n_] := b[n] = If[n==0, 1, Sum[b[n-i]*Binomial[n-1, i-1]/i!^2, {i, 1, n}]];

a[n_] := b[n]*n!^2;

Table[a[n], {n, 0, 20}] (* Jean-Fran├žois Alcover, Mar 14 2017, after Alois P. Heinz *)

PROG

(PARI) {a(n)=n!^3*polcoeff(exp(sum(m=1, n, x^m/m!^3)+x*O(x^n)), n)} /* Paul D. Hanna, Mar 15 2012 */

CROSSREFS

Probably A061698 from the same paper is an erroneous version of this sequence. - Les Reid, Jan 01 2011

Column k=3 of A275043.

Row sums of A061692.

Sequence in context: A192558 A179156 A196304 * A061698 A238631 A220557

Adjacent sequences:  A061681 A061682 A061683 * A061685 A061686 A061687

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 18 2001

EXTENSIONS

More terms from Karol A. Penson, Sep 10 2001

STATUS

approved

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Last modified January 25 19:09 EST 2020. Contains 331249 sequences. (Running on oeis4.)