A128577 Self-convolution of A128318.

1, 2, 9, 64, 624, 7736, 116416, 2060808, 41952600, 965497440, 24786054816, 702201877920, 21761251764672, 732269872931712, 26589359234860560, 1036241806935453696, 43142510740036313088, 1911022260200150482944, 89737455913330610995200, 4452805047268938247981056, 232806644343118618035904512, 12791828071344703747110764544, 736928909474399720669590216704, 44416721474748725213260027514880

Offset: 0

Author

Paul D. Hanna, Mar 11 2007

Keywords

• nonn

Comments

A128318 equals row 0 of table A128570.

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A128570 (triangle), rows: A128318, A128571, A128572, A128573, A128574, A128575, A128576; A128578 (main diagonal), A128579 (antidiagonal sums).

Programs

PARI

{a(n)=local(A=1+(n+1)*x);for(j=0,n,A=1+(n+1-j)*x*A^2 +x*O(x^n)); polcoeff(A^2,n)}
for(n=0, 25, print1(a(n), ", "))

Formula

G.f.: A(x) = [1 + x*R(x,1)^2]^2, where R(x,1) = 1 + 2*x*R(x,2)^2, R(x,2) = 1 + 3*x*R(x,3)^2, ..., R(x,n) = 1 + (n+1)*x*R(x,n+1)^2, ... and R(x,n) is the g.f. of row n of table A128570.

a(n) ~ 2*A128318(n). - Vaclav Kotesovec, Mar 19 2016