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
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..273
- Eric Weisstein's MathWorld, Stirling Transform.
- Eric Weisstein's MathWorld, Bell Polynomial.
Programs
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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
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Mathematica
Table[Sum[(n + 1)!/(k + 1) StirlingS2[n, k], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *) -
PARI
a(n)=round((n+1)!*exp(-1)*sum(i1=0,200, sum(i2=i1+1,200,i1^n*1./i2!)))
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
Extensions
Typo in name corrected by Vladimir Reshetnikov, Oct 20 2015