A009635 Expansion of e.g.f. tan(x*exp(x)).

0, 1, 2, 5, 28, 201, 1566, 14349, 154456, 1870225, 25034650, 368887573, 5938767924, 103580577881, 1945112687350, 39137964503837, 840076566197552, 19158967944112929, 462642378426338994, 11792392190823752229

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A009017, A009448, A009768, A191719.

Programs

Mathematica

terms = 20;
egf = Tan[x*Exp[x]] + O[x]^terms ;
CoefficientList[egf, x] Range[0, terms - 1]! (* Jean-François Alcover, Sep 24 2019 *)

Maxima

a(n):=2*sum(binomial(n,2*m+1)*(2*m+1)^(n-2*m-1)*sum(j!*2^(2*m-j)*(-1)^(m+1+j)*stirling2(2*m+1,j),j,1,2*m+1),m,0,(n-1)/2); /* Vladimir Kruchinin, Jun 10 2011 */

Formula

a(n) = 2*Sum_{m=0..floor((n-1)/2)} binomial(n, 2*m+1)*(2*m+1)^(n-2*m-1 * Sum_{j=1..2*m+1} j!*2^(2*m-j)*(-1)^(m+1+j)*Stirling2(2*m+1, j)). - Vladimir Kruchinin, Jun 10 2011

Extensions

Extended, reformatted, offset corrected 03/97.