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A182934 Generalized Bell numbers, column 2 of A182933. 2
1, 2, 27, 778, 37553, 2688546, 265141267, 34260962282, 5594505151713, 1123144155626338, 271300013006911211, 77489174023697484522, 25797166716252173322577, 9890278784047791697198658, 4322087630240844404678150883 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 29 2013 *)

CROSSREFS

Cf. A182933, A000262.

Sequence in context: A090248 A300591 A251693 * A078102 A221534 A221535

Adjacent sequences:  A182931 A182932 A182933 * A182935 A182936 A182937

KEYWORD

nonn

AUTHOR

Peter Luschny, Mar 29 2011

STATUS

approved

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Last modified January 22 10:25 EST 2020. Contains 331144 sequences. (Running on oeis4.)