A218504 - OEIS

%I #12 Mar 20 2016 11:37:40

%S 1,1,3,9,40,200,1286,9002,74712,672408,6892312,75815432,925733216,

%T 12034531808,170656068480,2559841027200,41356302857344,

%U 703057148574848,12752569691858048,242298824145302912,4875886476833445888,102393616013502363648,2264106940756915715584

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

%H Vaclav Kotesovec, <a href="/A218504/b218504.txt">Table of n, a(n) for n = 0..410</a>

%F E.g.f.: 1/(1-x) * Product_{n>=1} cosh(x^n/n); see A130268.

%F a(n) ~ c * n!, where c = A249673 = Product_{k>=1} cosh(1/k) = 2.1164655365... . - _Vaclav Kotesovec_, Nov 03 2014

%e E.g.f.: A(x) = 1 + x + 3*x^2/2! + 9*x^3/3! + 40*x^4/4! + 200*x^5/5! +...

%e where A(x) = 1/((1-tanh(x))*(1-tanh(x^2/2))*(1-tanh(x^3/3))*(1-tanh(x^4/4))*...)

%e Let G(x) = Product_{n>=1} cosh(x^n/n) be the e.g.f. of A130268:

%e G(x) = 1 + x^2/2! + 4*x^4/4! + 86*x^6/6! + 2696*x^8/8! + 168232*x^10/10! +...

%e then e.g.f. A(x) = G(x)/(1-x).

%t 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 *)

%o (PARI) {a(n)=n!*polcoeff(1/prod(k=1, n, (1-tanh(x^k/k+x*O(x^n)))), n)}

%o for(n=0,30,print1(a(n),", "))

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 31 2012