A218504 E.g.f.: Product_{n>=1} 1/(1 - tanh(x^n/n)).

1, 1, 3, 9, 40, 200, 1286, 9002, 74712, 672408, 6892312, 75815432, 925733216, 12034531808, 170656068480, 2559841027200, 41356302857344, 703057148574848, 12752569691858048, 242298824145302912, 4875886476833445888, 102393616013502363648, 2264106940756915715584

Offset: 0

Author

Paul D. Hanna, Oct 31 2012

Keywords

• nonn

Examples

			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).
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..410

Crossrefs

Cf. A130263, A130268, A249673, A270597, A270598.

Programs

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 *)

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),", "))

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