A228193 G.f.: exp( Sum_{n>=1} A001850(n^2)*x^n/n ), where A001850 forms the central Delannoy numbers.

1, 3, 165, 488007, 63015285321, 313849204040245803, 57549960579131376060801997, 379048169979935686476204047966170767, 88353684521579654155696728418892273040483607185, 721871639878336367921338532273490438662977816273231098545619

Offset: 0

Author

Paul D. Hanna, Aug 15 2013

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 3*x + 165*x^2 + 488007*x^3 + 63015285321*x^4 +...
where the logarithm of the g.f. begins:
log(A(x)) = 3*x + 321*x^2/2 + 1462563*x^3/3 + 252055236609*x^4/4 +...+ A001850(n^2)*x^n/n +...
		

Crossrefs

Cf. A228192, A001850.

Programs

PARI

{A228192(n)=sum(k=0,n^2,binomial(n^2,k)*binomial(n^2+k,k))}
{a(n)=polcoeff(exp(sum(k=1,n+1,A228192(k)*x^k/k) +x*O(x^n)),n)}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative yields A228192.