OFFSET
0,4
FORMULA
a(n) = Sum(m=1..n, Sum(k=m..n, (((-1)^(k-m)+1)*(Sum(j=m..k, C(j-1,m-1)*j! *2^(k-j-1) *Stirling2(k,j)*(-1)^((m+k)/2+j)))*((-1)^(n-k)+1)*Sum(i=0..k/2, (2*i-k)^n *C(k,i)*(-1)^((n+k)/2-i)))/(2^k*k!))/m!). - Vladimir Kruchinin, May 05 2011
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[Tan[Sin[x]]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 25 2011 *)
PROG
(Maxima)
a(n):=sum(sum((((-1)^(k-m)+1)*(sum(binomial(j-1, m-1)*j!*2^(k-j-1) *stirling2(k, j)*(-1)^((m+k)/2+j), j, m, k))*((-1)^(n-k)+1)*sum((2*i-k)^n *binomial(k, i)*(-1)^((n+k)/2-i), i, 0, k/2))/(2^k*k!), k, m, n)/m!, m, 1, n); /* Vladimir Kruchinin, May 05 2011 */
(PARI)
x='x+O('x^66); /* that many terms */
egf=exp(tan(sin(x))); /* = 1 + x + 1/2*x^2 + 1/3*x^3 + 5/24*x^4 + ... */
Vec(serlaplace(egf)) /* show terms */ /* Joerg Arndt, May 05 2011 */
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
Definition corrected by Joerg Arndt, May 05 2011
STATUS
approved