A064312 a(n) = B(n)*P(n), where B(n) are Bell numbers (A000110) and P(n) are numbers of arrangements of a set of n elements (A000522).

1, 2, 10, 80, 975, 16952, 397271, 12014900, 453748140, 20859612270, 1143989113475, 73628313849840, 5486361777107965, 467931786713485382, 45238398292112762210, 4915902436799253089420, 596048018991814531136899

Offset: 0

Author

Karol A. Penson, Sep 07 2001

Keywords

• nonn

Crossrefs

Cf. A000110, A000522.

Programs

Maple

a:=n->sum(bell(n)*n!/j!,j=0..n):seq(a(n),n=0..16); # Zerinvary Lajos, Mar 19 2007

Formula

Integral representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)= int(x^n*sum(exp(-x/k)*Heaviside(x-k)/(k*k!), k=1..infinity), x=0..infinity).

E.g.f.: A(x) = Sum_{n>=0} exp(n*x-1)/(n!*(1-n*x)). - Vladeta Jovovic, Feb 04 2008