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A059386 Expansion of e.g.f. cosh(cosh(x)-1) (even powers only). 2

%I

%S 1,0,3,15,168,3405,77253,2151240,77493783,3369709995,169438618608,

%T 9847267355145,658888820876553,49985438650733040,4245160431876404043,

%U 401030532597501719655,41924382309752516224728,4820179120197824593864965

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

%C 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

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

%H G. C. Greubel, <a href="/A059386/b059386.txt">Table of n, a(n) for n = 0..250</a>

%p seq(factorial(k)*coeftayl(cosh(cosh(x)-1), x = 0, k),k=0..200,2); # _Muniru A Asiru_, Jan 29 2018

%t 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 *)

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

%o (PARI) 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

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jan 28 2001

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)