A093638 G.f. satisfies: A(x) = Product_{n>=0} 1/(1-a(n)*x^(n+1))^2 = Sum_{n>=0} a(n)*x^n.

1, 2, 7, 26, 109, 466, 2142, 9870, 47438, 228750, 1133373, 5618252, 28431660, 143809690, 738803296, 3794224624, 19718366257, 102416655624, 537315418006, 2816334685644, 14883569577907, 78603101910486, 417974689553235, 2220832056696030, 11871111721797874

Offset

0,2

Comments

Equals the self-convolution of A093639.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..184

Formula

G.f. satisfies: A(x) = exp( 2*Sum_{n>=1} Sum_{k>=1} a(k)^n * (x^k)^n /n ) = Sum_{n>=0} a(n)*x^n. - Paul D. Hanna, Feb 13 2013

Example

G.f.: A(x) = 1 + 2*x + 7*x^2 + 26*x^3 + 109*x^4 + 466*x^5 + 2142*x^6 +...
where
A(x) = 1/((1-x)*(1-2*x^2)*(1-7*x^3)*(1-26*x^4)*(1-109*x^4)*(1-466*x^4)*...)^2.

Prog

(PARI) a(n)=polcoeff(prod(i=0, n-1, 1/(1-a(i)*x^(i+1))^2)+x*O(x^n), n)
(PARI) a(n)=local(A=1+x); for(i=1, n, A=exp(2*sum(m=1, n, 1/m*sum(k=1, n, polcoeff(A+O(x^k), k-1)^m*x^(m*k)) +x*O(x^n)))); polcoeff(A, n)
for(n=0, 30, print1(a(n), ", ")) \\ Paul D. Hanna, Feb 13 2013

Crossrefs

Cf. A093637, A093639.

Sequence in context: A302184 A150578 A150579 * A150580 A150581 A150582

Adjacent sequences: A093635 A093636 A093637 * A093639 A093640 A093641

Keyword

nonn

Author

Paul D. Hanna, Apr 07 2004

Status

approved