A009672 Expansion of e.g.f. tan(sin(x)*exp(x)).

0, 1, 2, 4, 24, 172, 1192, 10176, 106176, 1212048, 15123872, 210069440, 3195595392, 52434870464, 926003117184, 17548224583168, 354716499392512, 7614573123195136, 173087393243492864, 4153672167748662272

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = 2*sum(k=0..(n-1)/2, ((sum(j=1..2*k+1, j!*2^(-j)*(-1)^(j)*stirling2(2*k+1,j)))*sum(r=k..(n-1)/2, binomial(n,n-1-2*r)*((2*k+1)^(n-1-2*r)*sum(i=0..(2*k+1)/2, (2*i-2*k-1)^(2*r+1)*binomial(2*k+1,i)*(-1)^(r-i)))))/(2*k+1)!). - Vladimir Kruchinin, Jun 13 2011

Mathematica

With[{nn=20}, CoefficientList[Series[Tan[Sin[x]Exp[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jul 31 2018 *)

Prog

(Maxima)
a(n):=2*sum(((sum(j!*2^(-j)*(-1)^(j)*stirling2(2*k+1, j), j, 1, 2*k+1))*sum(binomial(n, n-1-2*r)*((2*k+1)^(n-1-2*r)*sum((2*i-2*k-1)^(2*r+1)*binomial(2*k+1, i)*(-1)^(r-i), i, 0, (2*k+1)/2)), r, k, (n-1)/2))/(2*k+1)!, k, 0, (n-1)/2); /* Vladimir Kruchinin, Jun 13 2011 */

Crossrefs

Sequence in context: A110491 A019010 A275553 * A018988 A012587 A012292

Adjacent sequences: A009669 A009670 A009671 * A009673 A009674 A009675

Keyword

nonn,easy

Author

R. H. Hardin

Extensions

Extended and signs tested by Olivier Gérard, Mar 15 1997

Status

approved