A128572 Row 2 of table A128570.

1, 3, 24, 288, 4440, 82080, 1752000, 42178800, 1127335680, 33073099200, 1055891810880, 36435757294080, 1351364788224000, 53617083034314240, 2266453101278568960, 101705245560225146880, 4829501671573344393600

Offset: 0

Author

Paul D. Hanna, Mar 11 2007

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..370

Crossrefs

Cf. A128570 (triangle), other rows: A128318, A128571, A128573, A128574, A128575, A128576; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).

Programs

PARI

{a(n)=local(A=1+(n+3)*x);for(j=0,n,A=1+(n+3-j)*x*A^2 +x*O(x^n)); polcoeff(A,n)}

Formula

G.f.: A(x) = 1 + 3x*R(x,3)^2, where R(x,3) = 1 + 4*x*R(x,4)^2, R(x,4) = 1 + 5*x*R(x,5)^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) ~ 8*n^2*A128318(n)/9. - Vaclav Kotesovec, Mar 19 2016