A102244 a(n) = exp(-1) * (n+1)! * Sum_{i>j>=0} j^n/i!.

1, 1, 5, 42, 544, 10020, 246840, 7790160, 305234496, 14493790080, 818125056000, 54040182134400, 4122847701941760, 359308852504842240, 35434445974210483200, 3922092526740740352000, 483768942063738966835200, 66076388642496229027430400, 9938208084601523840431718400

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..273

Eric Weisstein's MathWorld, Stirling Transform.

Eric Weisstein's MathWorld, Bell Polynomial.

Formula

a(n) = Sum(k=0..n, (n+1)!/(k+1)*stirling2(n,k)). - Vladimir Reshetnikov, Oct 20 2015

a(n) = (n+1)!*Integrate(x=0..1, B_n(x)), where B_n(x) is n-th Bell polynomial. - Vladimir Reshetnikov, Oct 21 2015

Maple

seq(add((n+1)!/(k+1)*Stirling2(n, k), k=0..n), n=0..20); # Robert Israel, Oct 21 2015
# Using the triangle algorithm described in A363732:
b := proc(n, m, x) option remember; if n = 0 then (-1)^m/(m + 1)! else
-(n + 1) * ((m + 1)*b(n - 1, m + 1, x) - (m + 1 - x)*b(n - 1, m, x)) fi end:
a := n -> local k; add(coeff(b(n, 0, x), x, k), k = 0..n):
seq(a(n), n = 0..18); # Peter Luschny, Jun 20 2023

Mathematica

Table[Sum[(n + 1)!/(k + 1) StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *)

Prog

(PARI) a(n)=round((n+1)!*exp(-1)*sum(i1=0, 200, sum(i2=i1+1, 200, i1^n*1./i2!)))

Crossrefs

Cf. A000110, A363732.

Sequence in context: A108398 A370907 A239997 * A323313 A363435 A337593

Adjacent sequences: A102241 A102242 A102243 * A102245 A102246 A102247

Keyword

nonn

Author

Benoit Cloitre, Feb 18 2005

Extensions

Typo in name corrected by Vladimir Reshetnikov, Oct 20 2015

Status

approved