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

0,5

Links

Table of n, a(n) for n=0..19.

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

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

Crossrefs

Cf. A023998, A061697.

Sequence in context: A287303 A142216 A027005 * A062643 A245528 A253218

Adjacent sequences: A061693 A061694 A061695 * A061697 A061698 A061699

Keyword

nonn

Author

N. J. A. Sloane, Jun 19 2001

Extensions

More terms from Ilya Gutkovskiy, Jul 12 2020

Status

approved