OFFSET
0,2
FORMULA
a(n) = b(2*n+1) where b(n) = Sum_{k=1..n} (binomial(n,k)*(((-1)^(k-1)+1)*(Sum_{i=0..k} (k-2*i)^(n-k)*binomial(k,i))*Sum_{j=1..k} j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k,j))/(2^k)). - Vladimir Kruchinin, Apr 21 2011
MATHEMATICA
With[{nn=30}, Take[CoefficientList[Series[Tan[Cosh[x]*x], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Sep 06 2017 *)
PROG
(Maxima)
a(n):=b(2*n+1);
b(n):=sum(binomial(n, k)*(((-1)^(k-1)+1)*(sum((k-2*i)^(n-k)*binomial(k, i), i, 0, k))*sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k, j), j, 1, k))/(2^k), k, 1, n); /* Vladimir Kruchinin, Apr 21 2011 */
(PARI)
a(n)={n=2*n+1; sum(k=1, n, binomial(n, k)*(((-1)^(k-1)+1)*(sum(i=0, k, (k-2*i)^(n-k)*binomial(k, i)))*sum(j=1, k, j!*2^(k-j-1)*(-1)^((k+1)/2+j)* stirling(k, j, 2)))/(2^k)); } /* Kruchinin's formula; Joerg Arndt, Apr 22 2011 */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Extended and signs tested by Olivier Gérard, Mar 15 1997
Name corrected by Joerg Arndt, Apr 23 2011
Previous Mathematica program replaced by Harvey P. Dale, Sep 06 2017
STATUS
approved