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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 Adjacent sequences: A009631 A009632 A009633 * A009635 A009636 A009637 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 December 6 04:35 EST 2022. Contains 358594 sequences. (Running on oeis4.)