A168405 E.g.f.: Sum_{n>=0} arcsin(2^n*x)^n/n!.

1, 2, 16, 520, 66560, 33882400, 69055283200, 564153087455360, 18462510039810703360, 2418626471936038215754240, 1267795676362601991645220044800, 2658560574070850656450883768752998400

Offset: 0

Author

Paul D. Hanna, Nov 25 2009

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + 2*x + 16*x^2/2! + 520*x^3/3! + 66560*x^4/4! + ...
A(x) = 1 + arcsin(2*x) + arcsin(4*x)^2/2! + arcsin(8*x)^3/3! + arcsin(16*x)^4/4! + ... + arcsin(2^n*x)^n/n! + ...
a(n) = coefficient of x^n/n! in G(x)^(2^n) where G(x) = exp(arcsin(x)):
G(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 20*x^5/5! + 85*x^6/6! + ... + A006228(n)*x^n/n! + ...
		

Crossrefs

Cf. A006228 (exp(arcsin x)), variants: A136632, A168402, A168403, A168404, A168406, A168407, A168408.

Programs

PARI

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

PARI

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

Formula

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