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A258114 E.g.f.: Sum_{n>=0} x^n * cosh(n*x).

%I A258114 #15 Oct 19 2017 03:43:42
%S A258114 1,1,2,9,72,665,6960,85057,1199744,19070865,336372480,6522635801,
%T A258114 137996694528,3163206890857,78085740701696,2065239729737745,
%U A258114 58263449436979200,1746433243580269217,55428341343200280576,1856918215298125692073,65483209810866254643200,2424691204935999655757241
%N A258114 E.g.f.: Sum_{n>=0} x^n * cosh(n*x).
%H A258114 G. C. Greubel, <a href="/A258114/b258114.txt">Table of n, a(n) for n = 0..410</a>
%F A258114 E.g.f.: (1 - x*cosh(x)) / (1 - 2*x*cosh(x) + x^2).
%F A258114 a(n) = Sum_{k=0..n} n!/k! * ((n-k)^k + (-n+k)^k)/2.
%F A258114 a(n) ~ n! * (1-c*cosh(c)) / (2*(cosh(c)+c*(sinh(c)-1)) * c^(n+1)), where c = A030178 = LambertW(1) = 0.56714329040978387299996866... . - _Vaclav Kotesovec_, May 21 2015
%e A258114 E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 72*x^4/4! + 665*x^5/5! +...
%e A258114 where A(x) = 1 + x*cosh(x) + x^2*cosh(2*x) + x^3*cosh(3*x) + x^4*cosh(4*x) +...
%t A258114 CoefficientList[Series[(1-x*Cosh[x])/(1-2*x*Cosh[x]+x^2), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, May 21 2015 *)
%o A258114 (PARI) {a(n) = sum(k=0,n, n!/k! * ((n-k)^k + (-n+k)^k)/2)}
%o A258114 for(n=0,30,print1(a(n),", "))
%o A258114 (PARI) {a(n) = local(A=1); A = sum(m=0,n, x^m*cosh(m*x +x*O(x^n))); n!*polcoeff(A,n)}
%o A258114 for(n=0,30,print1(a(n),", "))
%o A258114 (PARI) {a(n) = local(X=x+x*O(x^n),A=1); A = (1 - x*cosh(X)) / (1 - 2*x*cosh(X) + x^2); n!*polcoeff(A,n)}
%o A258114 for(n=0,30,print1(a(n),", "))
%Y A258114 Cf. A030178.
%K A258114 nonn
%O A258114 0,3
%A A258114 _Paul D. Hanna_, May 20 2015