A133316 G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n/(1+x)^(n^2).

1, 1, 2, 8, 54, 544, 7508, 133704, 2943194, 77589536, 2391477804, 84582890704, 3382005372970, 151034046369696, 7458091839548356, 403808650013237224, 23801728042233670770, 1517930142778063770304, 104179592763803229618620

Offset: 0

Author

Paul D. Hanna, Dec 24 2010

Keywords

• nonn

Examples

			1/(1-x) = 1 + x/(1+x) + 2*x^2/(1+x)^4 + 8*x^3/(1+x)^9 + 54*x^4/(1+x)^16 +...
		

Crossrefs

Cf. A141761, A177447, A215241, A215242, A215243.

Programs

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^2)),n))}

PARI

{a(n)=if(n==0, 1, 1 - sum(j=0, n-1, a(j)*(-1)^(n-j)*binomial(j^2+n-j-1, n-j)))}

Formula

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