A227820 G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n * Sum_{k=0..n} binomial(n,k)^2 * (-x)^k*(1+x)^(n-k).

1, 1, 1, 3, 21, 271, 5547, 163449, 6515653, 336521487, 21811917243, 1731102129033, 164965649015727, 18576187504063053, 2439032446517056113, 369203184490259386011, 63808807042506278660325, 12485211237616581137265679, 2745317734648664454455184459

Offset

0,4

Links

Table of n, a(n) for n=0..18.

Example

1/(1-x) = 1 + x*((1+x) - x)
+ x^2*((1+x)^2 - 2^2*x*(1+x) + x^2)
+ 3*x^3*((1+x)^3 - 3^2*x*(1+x)^2 + 3^2*x^2*(1+x) - x^3)
+ 21*x^4*((1+x)^4 - 4^2*x*(1+x)^3 + 6^2*x^2*(1+x)^2 - 4^2*x^3*(1+x) + x^4)
+ 271*x^5*((1+x)^5 - 5^2*x*(1+x)^4 + 10^2*x^2*(1+x)^3 - 10^2*x^3*(1+x)^2 + 5^2*x^4*(1+x) - x^5) + ...

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)^(k-j)+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A227821.

Sequence in context: A269938 A277454 A215127 * A336809 A066206 A130032

Adjacent sequences: A227817 A227818 A227819 * A227821 A227822 A227823

Keyword

nonn

Author

Paul D. Hanna, Jul 31 2013

Status

approved