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 A061685 Generalized Bell numbers. 3
 1, 1, 9, 298, 25097, 4383626, 1394519922, 738298190981, 608765840524809, 742996254490626106, 1289282092211451157634, 3078466688415490018129781, 9844321075186192301310239858, 41209705023068976933023104392293, 221473347301087557264532943397984133 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..167 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 a(n) = Sum_{pi} n!/(k(1)! * 1!^k(1) * k(2)! * 2!^k(2) * ... * k(n)! * n!^k(n)) * (n!/(1!^k(1) * 2!^k(2) * ... * n!^k(n)))^L, where pi runs through all partitions k(1) + 2 * k( 2) + ... + n * k(n) = n, with L = 3. MAPLE b:= proc(n) option remember; `if`(n=0, 1,       add(b(n-i)*binomial(n-1, i-1)/i!^3, i=1..n))     end: a:= n-> b(n)*n!^3: 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!^3, {i, n}]]; a[n_] := b[n]*n!^3; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 15 2017, after Alois P. Heinz *) CROSSREFS Column k=4 of A275043. Sequence in context: A216966 A211077 A211082 * A183549 A104775 A106663 Adjacent sequences:  A061682 A061683 A061684 * A061686 A061687 A061688 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 18 2001 EXTENSIONS Formula and more terms from Vladeta Jovovic, Dec 09 2001 STATUS approved

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Last modified January 17 23:37 EST 2020. Contains 330995 sequences. (Running on oeis4.)