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

0,4

Links

Table of n, a(n) for n=0..24.

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

Example

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! +...

Prog

(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)}

Crossrefs

Cf. A138315.

Sequence in context: A002216 A024717 A003724 * A115277 A130221 A036782

Adjacent sequences: A138311 A138312 A138313 * A138315 A138316 A138317

Keyword

nonn

Author

Paul D. Hanna, Mar 13 2008

Status

approved