A168402 E.g.f.: Sum_{n>=0} tanh(2^n*x)^n/n!.

1, 2, 16, 496, 63488, 32899584, 68048945152, 560546063546368, 18415227534711980032, 2416302301874471529480192, 1267360472364492854214927581184, 2658246833130441862918267501949222912

Offset: 0

Author

Paul D. Hanna, Nov 25 2009

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 496*x^3/3! + 63488*x^4/4! +...
A(x) = 1 + tanh(2*x) + tanh(4*x)^2/2! + tanh(8*x)^3/3! + tanh(16*x)^4/4! +...+ tanh(2^n*x)^n/n! +...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(tanh(x)):
G(x) = 1 + x + x^2/2! - x^3/3! - 7*x^4/4! - 3*x^5/5! + 97*x^6/6! + 275*x^7/7! +...+ A003723(n)*x^n/n! +...
		

Crossrefs

Cf. A003723 (exp(tanh x)), variant: A136632.

Programs

Mathematica

nmax = 15; CoefficientList[Series[Sum[Tanh[2^k*x]^k/k!, {k, 0, nmax}], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Oct 11 2020 *)

PARI

{a(n)=n!*polcoeff(sum(k=0,n,tanh(2^k*x +x*O(x^n))^k/k!),n)}

PARI

{a(n)=n!*polcoeff(exp(2^n*tanh(x +x*O(x^n))),n)}

Formula

a(n) = [x^n/n! ] exp(2^n*tanh(x)).

a(n) ~ 2^(n^2). - Vaclav Kotesovec, Oct 11 2020

Extensions

Example corrected by Paul D. Hanna, Nov 25 2009