A182952 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n*(3*n-1)/2).

1, 1, 2, 10, 92, 1314, 26216, 682006, 22067246, 858473488, 39151350362, 2052833191416, 121860108702876, 8088426308992214, 594165066779656784, 47891997458689633520, 4205027188507582359156, 399677541092136186656238

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = 1 - Sum_{k=0..n-1} a(k)*(-1)^(n-k)*C(k(3k-1)/2 + n-k-1, n-k) for n>0, with a(0)=1.

Example

1/(1-x) = 1 + x/(1+x) + 2*x^2/(1+x)^5 + 10*x^3/(1+x)^12 + 92*x^4/(1+x)^22 + 1314*x^5/(1+x)^35 + 26216*x^6/(1+x)^51 +...

Prog

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

Crossrefs

Cf. A133316, A182951, A182956, A141761.

Sequence in context: A277380 A108528 A181136 * A108209 A111773 A289020

Adjacent sequences: A182949 A182950 A182951 * A182953 A182954 A182955

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2010

Status

approved