A182951 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n^2+n).

1, 1, 3, 16, 134, 1596, 25193, 501236, 12118038, 346373740, 11460810227, 431732603292, 18269225018646, 858920382899880, 44455946598501069, 2513531512113074244, 154218539815668325502, 10209332972405039928876

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^2+k + n-k-1, n-k) for n>0, with a(0)=1.

Example

1/(1-x) = 1 + x/(1+x)^2 + 3*x^2/(1+x)^6 + 16*x^3/(1+x)^12 + 134*x^4/(1+x)^20 +...

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*(m+1))), n))}
(PARI) {a(n)=if(n==0, 1, 1 - sum(j=0, n-1, a(j)*(-1)^(n-j)*binomial(j*(j+1)+n-j-1, n-j)))}

Crossrefs

Cf. A182952, A133316, A141761.

Sequence in context: A119392 A307979 A129043 * A247770 A357088 A277673

Adjacent sequences: A182948 A182949 A182950 * A182952 A182953 A182954

Keyword

nonn

Author

Paul D. Hanna, Dec 31 2010

Status

approved