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A009634 E.g.f. tan(x*cosh(x)), zeros omitted. 5
1, 5, 81, 3429, 238273, 25669093, 3923627345, 807194393477, 215176572950017, 72120516857475141, 29686285367774651089, 14721686852776234894885, 8656857857596485141973441, 5955926696414663185424979749 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
Sequence in context: A009756 A336807 A188419 * A165435 A197443 A337852
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

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)