A203716 E.g.f.: Product_{n>=1} (exp(2*x^n) + 1)/2.

1, 1, 4, 16, 104, 696, 6272, 57856, 652416, 7657600, 104244992, 1475430144, 23426373632, 387521615872, 7034561925120, 132850810138624, 2709375373672448, 57456525327335424, 1301169515685085184, 30573796812553584640, 760486440376336908288, 19600568102376899608576

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Example

E.g.f.: A(x) = 1 + x + 4*x^2/2! + 16*x^3/3! + 104*x^4/4! + 696*x^5/5! +...
where the e.g.f. equals the product:
A(x) = (exp(2*x)+1)/2 * (exp(2*x^2)+1)/2 * (exp(2*x^3)+1)/2 * (exp(2*x^4)+1)/2 *...
The log of the e.g.f. begins:
log(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 +...+ A203715(n)*x^n/n! +...
Note that the coefficients of the odd powers of x in log(A(x)) equals 1.

Mathematica

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

Prog

(PARI) {a(n)=n!*polcoeff(prod(k=1, n, (exp(2*x^k+x*O(x^n))+1)/2), n)}

Crossrefs

Cf. A203715 (log), A203709, A270664, A270665, A270666.

Sequence in context: A094637 A332783 A332773 * A330537 A136793 A274889

Adjacent sequences: A203713 A203714 A203715 * A203717 A203718 A203719

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2012

Status

approved