A227821 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n/(1-x)^n * Sum_{k=0..n} binomial(n,k)^2 * (-x)^k.

1, 1, 1, 3, 23, 319, 6857, 209259, 8563855, 451423559, 29740026091, 2391941092881, 230478978551687, 26197466746328951, 3467374262207936333, 528520864124393733623, 91899269489447224280211, 18078003975588275698610731, 3994026796748854058413543011, 984658830428133667413074092081

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Example

1/(1-x) = 1 + x*(1-x)/(1-x)
+ x^2*(1 - 2^2*x + x^2)/(1-x)^2
+ 3*x^3*(1 - 3^2*x + 3^2*x^2 - x^3)/(1-x)^3
+ 23*x^4*(1 - 4^2*x + 6^2*x^2 - 4^2*x^3 + x^4)/(1-x)^4
+ 319*x^5*(1 - 5^2*x + 10^2*x^2 - 10^2*x^3 + 5^2*x^4 - x^5)/(1-x)^5
+ 6857*x^6*(1 - 6^2*x + 15^2*x^2 - 20^2*x^3 + 15^2*x^4 - 6^2*x^5 + x^6)/(1-x)^6 +...

Prog

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

Crossrefs

Cf. A227820.

Sequence in context: A356872 A088692 A188313 * A222076 A338301 A129458

Adjacent sequences: A227818 A227819 A227820 * A227822 A227823 A227824

Keyword

nonn

Author

Paul D. Hanna, Jul 31 2013

Status

approved