A226706 G.f.: 1 / sqrt(1 + 12*x*G(x)^4 - 16*x*G(x)^5) where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.

1, 2, 22, 256, 3174, 40862, 539376, 7247448, 98684230, 1357638124, 18831752122, 262974273200, 3692853486768, 52102851020154, 738102882420440, 10492839572260176, 149623214762194182, 2139329701502229300, 30661862088900836964, 440404155129948147776

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

Sum_{k=0..n} a(n-k)*a(k) = Sum_{k=0..n} C(3*n+2*k,n-k)*C(3*n-2*k,k).

Self-convolution equals A226705.

Example

G.f.: A(x) = 1 + 2*x + 22*x^2 + 256*x^3 + 3174*x^4 + 40862*x^5 +...
A related series is G(x) = 1 + x*G(x), which begins
G(x) = 1 + x + 6*x^2 + 51*x^3 + 506*x^4 + 5481*x^5 + 62832*x^6 +...
where A(x) = 1/sqrt(1 + 12*x*G(x)^4 - 16*x*G(x)^5).

Prog

(PARI) {a(n)=local(G=1+x); for(i=0, n, G=1+x*G^6+x*O(x^n)); polcoeff(1/sqrt(1+12*x*G^4-16*x*G^5), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A226705, A183160, A002295.

Sequence in context: A082777 A229465 A072076 * A036841 A307852 A365529

Adjacent sequences: A226703 A226704 A226705 * A226707 A226708 A226709

Keyword

nonn

Author

Paul D. Hanna, Jun 15 2013

Status

approved