A059385 Expansion of e.g.f. sinh(cosh(x)-1), (even terms only).

0, 1, 1, 16, 211, 3151, 73096, 2222221, 78804181, 3328776376, 168350871991, 9890935452091, 660814861059376, 49911348691790041, 4239141233825894761, 401191146623474166976, 41953203382631444827771, 4820014734080867077534471

Offset

0,4

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 7th line of table.

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Formula

a(n) = b(2*n) where b(n) = ((-1)^n+1)/4*Sum(k=1..n/2, ((Sum(j=1..k,((Sum(i=0..j,(j-2*i)^n*binomial(j,i)))*(-1)^(k-j)*binomial(k,j) )/2^(j)))*(1-(-1)^k)/(k!))). - Vladimir Kruchinin, Apr 23 2011

Mathematica

With[{nn = 50}, CoefficientList[Series[Sinh[Cosh[x] - 1], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* G. C. Greubel, Jan 29 2018 *)

Prog

(Maxima)
a(n):=b(2*n);
b(n):=((-1)^n+1)/4*sum(((sum(((sum((j-2*i)^n*binomial(j, i), i, 0, j))*(-1)^(k-j)*binomial(k, j))/2^(j), j, 1, k))*(1-(-1)^k)/(k!)), k, 1, n/2);
  /* Vladimir Kruchinin, Apr 23 2011 */
(PARI) x='x+O('x^50); v=Vec(serlaplace(sinh(cosh(x)-1))); concat([0], vector(#v\2, n, v[2*n-1])) \\ G. C. Greubel, Jan 29 2018

Crossrefs

Sequence in context: A295712 A319236 A222447 * A009440 A284226 A282395

Adjacent sequences: A059382 A059383 A059384 * A059386 A059387 A059388

Keyword

nonn

Author

N. J. A. Sloane, Jan 28 2001

Status

approved