A195509 Expansion of e.g.f. (exp(x*exp(x)) + exp(x/exp(x)))/2.

1, 1, 1, 4, 25, 96, 481, 3368, 20721, 141760, 1146721, 9098112, 77652169, 726208640, 6891125697, 69344336896, 738718169569, 8076031881216, 92647353941569, 1106883171037184, 13616813607795321, 174298975125127168, 2304515271134124577

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..541

Formula

E.g.f.: Sum_{n>=0} x^n*cosh(n*x)/n!.

a(n) = Sum_{m=0..floor((n-1)/2)} binomial(n,2*m)*(n-2*m)^(2*m) for n >= 1. - _Vladimir Kruchinin_, Mar 10 2013 [Edited by _Petros Hadjicostas_, May 06 2020]

Example

E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 25*x^4/4! + 96*x^5/5! + 481*x^6/6! +...

Maple

a := proc(n) local m: add(binomial(n, 2*m)*(n - 2*m)^(2*m), m = 0 .. floor(1/2*n - 1/2)): end proc:
seq(a(n), n = 1..30); # _Petros Hadjicostas_, May 06 2020 (for n >= 1)

Prog

(PARI) {a(n)=local(X=x+x*O(x^n), A=1+X); A=(exp(X*exp(X))+exp(X/exp(X)))/2; n!*polcoeff(A, n)}
(PARI) {a(n)=n!*polcoeff(sum(m=0, n, x^m*cosh(m*x+x*O(x^n))/m!), n)}
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^(2*k)*binomial(n, 2*k)); \\ _Seiichi Manyama_, Feb 15 2023

Crossrefs

Cf. A218296, A277464.

Sequence in context: A027764 A095669 A323967 * A027949 A226547 A264167

Adjacent sequences: A195506 A195507 A195508 * A195510 A195511 A195512

Keyword

nonn

Author

_Paul D. Hanna_, Sep 19 2011

Status

approved