A168406 E.g.f.: Sum_{n>=0} arctan(2^n*x)^n/n!.

1, 2, 16, 496, 63488, 32899840, 68049141760, 560546415810560, 18415229458563727360, 2416302337337071616327680, 1267360474688679165942982246400, 2658246833688954938616062542151680000

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 + arctan(2*x) + arctan(4*x)^2/2! + arctan(8*x)^3/3! + arctan(16*x)^4/4! + ... + arctan(2^n*x)^n/n! + ...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(arctan(x)):
G(x) = 1 + x + x^2/2! - x^3/3! - 7*x^4/4! + 5*x^5/5! + 145*x^6/6! + ... + A002019(n)*x^n/n! + ...
		

Crossrefs

Cf. A002019 (exp(arctan x)), variants: A136632, A168402, A168403, A168404, A168405, A168407, A168408.

Programs

PARI

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

PARI

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

Formula

a(n) = [x^n/n!] exp(2^n*arctan(x)) for n >= 0.