login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A059606
Expansion of (1/2)*(exp(2*x)-1)*exp(exp(x)-1).
8
0, 1, 4, 16, 68, 311, 1530, 8065, 45344, 270724, 1709526, 11376135, 79520644, 582207393, 4453142140, 35500884556, 294365897104, 2533900264547, 22604669612078, 208656457858161, 1990060882027600
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
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