A182934 Generalized Bell numbers, column 2 of A182933.

1, 2, 27, 778, 37553, 2688546, 265141267, 34260962282, 5594505151713, 1123144155626338, 271300013006911211, 77489174023697484522, 25797166716252173322577, 9890278784047791697198658, 4322087630240844404678150883

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = exp(-1)*n!^2*F_2([n+1,n+1],[1,2] |1), F_2 the generalized hypergeometric function of type 2_F_2.

Let b_{n}(x) = Sum_{j>=0}(x*exp((j+n-1)!/(j-1)!-1)/j!) then a(n) = 2 [x^2] series b_{n}(x), where [x^2] denotes the coefficient of x^2 in the Taylor series for b_{n}(x).

Maple

A182934 := proc(n)
exp(-x)*n!^2*hypergeom([n+1, n+1], [1, 2], x); round(evalf(subs(x=1, %), 66)) end:
seq(A182934(n), n=0..14);

Mathematica

a[n_] := n!^2*HypergeometricPFQ[{n+1, n+1}, {1, 2}, 1.`40.]/E; Table[a[n] // Round, {n, 0, 14}] (* Jean-François Alcover, Jul 29 2013 *)

Crossrefs

Cf. A182933, A000262.

Sequence in context: A300591 A377893 A251693 * A078102 A221534 A221535

Adjacent sequences: A182931 A182932 A182933 * A182935 A182936 A182937

Keyword

nonn

Author

Peter Luschny, Mar 29 2011

Status

approved