A138314 E.g.f. satisfies: A(x) = exp( Sum_{n>=0} a(n)*x^(2n+1)/(2n+1)! ).

1, 1, 1, 2, 5, 12, 37, 129, 465, 1912, 8449, 39481, 200081, 1069470, 6043361, 36120082, 226063729, 1484564600, 10184907985, 72814137773, 542009067393, 4188018707130, 33562233856177, 278441210021464, 2387929437251657

Offset: 0

Author

Paul D. Hanna, Mar 13 2008

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 12*x^5/5! + 37*x^6/6! +...
Log(A(x)) = x + x^3/3! + x^5/5! + 2*x^7/7! + 5*x^9/9! + 12*x^11/11! + 37*x^13/13! +...
		

Crossrefs

Cf. A138315.

Programs

PARI

{a(n)=local(A=if(n==0,x,sum(k=0,n\2,a(k)*x^(2*k+1)/(2*k+1)!))); n!*polcoeff(exp(A+x*O(x^n)),n)}

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(k) * a(n-2*k-1). - Ilya Gutkovskiy, Feb 25 2022