A203715 E.g.f.: Sum_{n>=1} log((1 + exp(2*x^n))/2).

1, 3, 6, 34, 120, 1096, 5040, 56848, 362880, 5451136, 39916800, 688876288, 6227020800, 130789805056, 1307674368000, 29497569445888, 355687428096000, 9746045395173376, 121645100408832000, 3451902721622867968, 51090942171709440000, 1686006043164464644096

Offset: 1

Author

Paul D. Hanna, Jan 04 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = x + 3*x^2/2! + x^3 + 34*x^4/4! + x^5 + 1096*x^6/6! + x^7 + 56848*x^8/8! + x^9 + 5451136*x^10/10! + x^11 +...
where A(x) = log((1+exp(2*x))/2) + log((1+exp(2*x^2))/2) + log((1+exp(2*x^3))/2) + log((1+exp(2*x^4))/2) +...
The exponentiation of the e.g.f. begins:
exp(A(x)) = 1 + x + 4*x^2/2! + 16*x^3/3! + 104*x^4/4! + 696*x^5/5! + 6272*x^6/6! + 57856*x^7/7! + 652416*x^8/8! +...+ A203716(n)*x^n/n! +...
		

Crossrefs

Cf. A203709, A203716 (exp).

Programs

Mathematica

nmax = 25; Rest[Range[0, nmax]! * CoefficientList[Series[Sum[Log[1/(1 - Tanh[x^k])], {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Mar 21 2016 *)

PARI

{a(n)=n!*polcoeff(sum(m=1,n,log((1+exp(2*x^m+x*O(x^n)))/2)),n)}

Formula

a(2*n-1) = (2*n-1)!.