A061696 Generalized Bell numbers.

1, 0, 1, 1, 19, 101, 1776, 23717, 515971, 11893597, 346475728, 11497161545, 444592761746, 19536147771219, 970739908493421, 54010183143383066, 3341831947578263267, 228462339968313577341, 17160142419913160027448, 1409008382280004776187961

Offset: 0

Author

N. J. A. Sloane, Jun 19 2001

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A023998, A061697.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(BesselI(0,2*sqrt(x)) - 1 - x). - Ilya Gutkovskiy, Jul 12 2020

Extensions

More terms from Ilya Gutkovskiy, Jul 12 2020