OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..410
FORMULA
E.g.f.: 1/(1-x) * Product_{n>=1} cosh(x^n/n); see A130268.
a(n) ~ c * n!, where c = A249673 = Product_{k>=1} cosh(1/k) = 2.1164655365... . - Vaclav Kotesovec, Nov 03 2014
EXAMPLE
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 9*x^3/3! + 40*x^4/4! + 200*x^5/5! +...
where A(x) = 1/((1-tanh(x))*(1-tanh(x^2/2))*(1-tanh(x^3/3))*(1-tanh(x^4/4))*...)
Let G(x) = Product_{n>=1} cosh(x^n/n) be the e.g.f. of A130268:
G(x) = 1 + x^2/2! + 4*x^4/4! + 86*x^6/6! + 2696*x^8/8! + 168232*x^10/10! +...
then e.g.f. A(x) = G(x)/(1-x).
MATHEMATICA
nn = 25; Range[0, nn]! * CoefficientList[Series[1/(1 - x)*Product[Cosh[x^k/k], {k, 1, nn}], {x, 0, nn}], x] (* Vaclav Kotesovec, Mar 20 2016 *)
PROG
(PARI) {a(n)=n!*polcoeff(1/prod(k=1, n, (1-tanh(x^k/k+x*O(x^n)))), n)}
for(n=0, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 31 2012
STATUS
approved