A061683 Generalized Bell numbers.

1, 1, 4, 37, 641, 18276, 789377, 48681011, 4101601933, 456231359098, 65186917527755, 11698971297097514, 2588414536916535692, 694943711701146526685, 223358454122075825673083, 84933806339641062320374739, 37818769294977584683919425677

Offset

0,3

Links

Table of n, a(n) for n=0..16.

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) = (n+1) * (n!)^2 * [z^0] (d^n/dz^n) exp(-1 + Sum_{k>=0} z^k/((k+1)*(k!)^3)). - Sean A. Irvine, Feb 27 2023

Crossrefs

Sequence in context: A094408 A348860 A352469 * A084283 A163880 A183509

Adjacent sequences: A061680 A061681 A061682 * A061684 A061685 A061686

Keyword

nonn

Author

N. J. A. Sloane, Jun 18 2001

Extensions

More terms from Sean A. Irvine, Feb 27 2023

Status

approved