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

0,2

Comments

A128318 equals row 0 of table A128570.

Links

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

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

Prog

(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), ", "))

Crossrefs

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

Sequence in context: A269770 A269649 A335517 * A052514 A274395 A036776

Adjacent sequences: A128574 A128575 A128576 * A128578 A128579 A128580

Keyword

nonn

Author

Paul D. Hanna, Mar 11 2007

Status

approved