OFFSET
0,3
COMMENTS
Starting (1, 4, 16, 68, 311, ...), = A008277 * A000217, i.e., the product of the Stirling2 triangle and triangular series. - Gary W. Adamson, Jan 31 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Vladeta Jovovic, More information.
FORMULA
a(n) = Sum_{i=0..n} Stirling2(n, i)*binomial(i+1, 2).
a(n) = (1/2)*(Bell(n+2)-Bell(n+1)-Bell(n)). - Vladeta Jovovic, Sep 23 2003
G.f.: Sum_{k>=1} (k*(k + 1)/2)*x^k/Product_{j=1..k} (1 - j*x). - Ilya Gutkovskiy, Jun 19 2018
a(n) ~ n^2 * Bell(n) / (2*LambertW(n)^2) * (1 - LambertW(n)/n). - Vaclav Kotesovec, Jul 28 2021
MAPLE
s := series(1/2*(exp(2*x)-1)*exp(exp(x)-1), x, 21): for i from 0 to 20 do printf(`%d, `, i!*coeff(s, x, i)) od:
MATHEMATICA
With[{nn=20}, CoefficientList[Series[((Exp[2x]-1)Exp[Exp[x]-1])/2, {x, 0, nn}] , x] Range[0, nn]!] (* Harvey P. Dale, Nov 10 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladeta Jovovic, Jan 29 2001
STATUS
approved