A171185 G.f.: exp( Sum_{n>=1} (x^n/n)*[Sum_{k=0..[n/2]} A034807(n,k)^3] ), where A034807 is a triangle of Lucas polynomials.

1, 1, 5, 14, 40, 126, 408, 1332, 4473, 15377, 53627, 189724, 680475, 2467975, 9038578, 33399571, 124400702, 466619283, 1761467038, 6688059913, 25527326897, 97901917060, 377123873505, 1458573962761, 5662223702216, 22056563938599

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Example

G.f.: A(x) = 1 + x + 5*x^2 + 14*x^3 + 40*x^4 + 126*x^5 + 408*x^6 +...
log(A(x)) = x + 9*x^2/2 + 28*x^3/3 + 73*x^4/4 + 251*x^5/5 + 954*x^6/6 +...+ A171215(n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (x^m/m)*sum(k=0, m\2, (binomial(m-k, k)+binomial(m-k-1, k-1))^3))+x*O(x^n)), n)}

Crossrefs

Cf. A171215, A093128, A171186.

Sequence in context: A023871 A274598 A327682 * A122485 A198086 A272018

Adjacent sequences: A171182 A171183 A171184 * A171186 A171187 A171188

Keyword

nonn

Author

Paul D. Hanna, Dec 14 2009

Status

approved