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

1, 1, 2, 9, 72, 665, 6960, 85057, 1199744, 19070865, 336372480, 6522635801, 137996694528, 3163206890857, 78085740701696, 2065239729737745, 58263449436979200, 1746433243580269217, 55428341343200280576, 1856918215298125692073, 65483209810866254643200, 2424691204935999655757241

Offset: 0

Author

Paul D. Hanna, May 20 2015

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 9*x^3/3! + 72*x^4/4! + 665*x^5/5! +...
where A(x) = 1 + x*cosh(x) + x^2*cosh(2*x) + x^3*cosh(3*x) + x^4*cosh(4*x) +...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..410

Crossrefs

Cf. A030178.

Programs

Mathematica

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 *)

PARI

{a(n) = sum(k=0,n, n!/k! * ((n-k)^k + (-n+k)^k)/2)}
for(n=0,30,print1(a(n),", "))

PARI

{a(n) = local(A=1); A = sum(m=0,n, x^m*cosh(m*x +x*O(x^n))); n!*polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))

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)}
for(n=0,30,print1(a(n),", "))

Formula

E.g.f.: (1 - x*cosh(x)) / (1 - 2*x*cosh(x) + x^2).

a(n) = Sum_{k=0..n} n!/k! * ((n-k)^k + (-n+k)^k)/2.

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