A180716 G.f.: 1 = Sum_{n>=0} a(n)*x^n * Sum_{k=0..n+1} C(n+1,k)^2*(-x)^k.

1, 1, 4, 35, 524, 11844, 374544, 15740121, 846918340, 56716282700, 4622924730800, 450422314335500, 51679784091622960, 6895215281303487760, 1058342987968671733824, 185145713675921057952219, 36616521252754210909572684, 8128356026325692474893812996

Offset: 0

Author

Paul D. Hanna, Sep 28 2010

Keywords

• nonn

Comments

Compare g.f. to a g.f. of the Catalan numbers (A000108):

1 = Sum_{n>=0} A000108(n)*x^n * Sum_{k=0..n+1} C(n+1,k)*(-x)^k.

Examples

			G.f.: 1 = 1*(1-x) + 1*x*(1-2^2*x+x^2) + 4*x^2*(1-3^2*x+3^2*x^2-x^3) + 35*x^3*(1-4^2*x+6^2*x^2-4^2*x^3+x^4) + 524*x^4*(1-5^2*x+10^2*x^2-10^2*x^3+5^2*x^4-x^5) +...
		

Crossrefs

Cf. A209440.

Programs

PARI

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