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A059385 Expansion of e.g.f. sinh(cosh(x)-1), (even terms only). 1
0, 1, 1, 16, 211, 3151, 73096, 2222221, 78804181, 3328776376, 168350871991, 9890935452091, 660814861059376, 49911348691790041, 4239141233825894761, 401191146623474166976, 41953203382631444827771, 4820014734080867077534471 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
REFERENCES
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 7th line of table.
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 28 2001
STATUS
approved

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Last modified July 12 22:19 EDT 2024. Contains 374257 sequences. (Running on oeis4.)