A059386 Expansion of e.g.f. cosh(cosh(x)-1) (even powers only).

1, 0, 3, 15, 168, 3405, 77253, 2151240, 77493783, 3369709995, 169438618608, 9847267355145, 658888820876553, 49985438650733040, 4245160431876404043, 401030532597501719655, 41924382309752516224728, 4820179120197824593864965

Offset

0,3

Comments

a(n) is the number of partitions of the set {1, 2, ..., 2n} into an even number of blocks, each containing an even number of elements. - Isabel C. Lugo (izzycat(AT)gmail.com), Aug 23 2004

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 9th line of table.

Links

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

Formula

a(0) = 1; a(n) = Sum_{i=1..floor(n/2)} 1/(2^(2*i-1)*(2*i)!) * Sum_{j=1..2*i} (-1)^j * j^(2*n) * binomial(4*i,2*i-j). - Seiichi Manyama, Jun 21 2026

Maple

seq(factorial(k)*coeftayl(cosh(cosh(x)-1), x = 0, k), k=0..200, 2); # Muniru A Asiru, Jan 29 2018

Mathematica

nn = 30; Insert[Select[Range[0, nn]! CoefficientList[Series[Cosh[Cosh[x] - 1], {x, 0, nn}], x], # > 0 &], 0, 2] (* Geoffrey Critzer, Mar 31 2012 *)
(* Alternative: *)
With[{nn = 50}, CoefficientList[Series[Cosh[Cosh[x] - 1], {x, 0, nn}], x] Range[0, nn]!][[1 ;; ;; 2]] (* G. C. Greubel, Jan 29 2018 *)

Prog

(PARI) my(x='x+O('x^50), v=Vec(serlaplace(cosh(cosh(x)-1)))); vector(#v\2, n, v[2*n-1]) \\ G. C. Greubel, Jan 29 2018

Crossrefs

Cf. A185951, A192060.

Sequence in context: A015013 A153280 A132683 * A077792 A153079 A173301

Adjacent sequences: A059383 A059384 A059385 * A059387 A059388 A059389

Keyword

nonn

Author

N. J. A. Sloane, Jan 28 2001

Status

approved