A128576 Row 6 of table A128570.

1, 7, 112, 2464, 65520, 1991808, 67189248, 2469837888, 97765355520, 4132860197760, 185458263419520, 8794132843507200, 439083652465543680, 23017956568726049280, 1263929372436815078400, 72550400791147384412160

Offset: 0

Author

Paul D. Hanna, Mar 11 2007

Keywords

• nonn

Comments

In general, row r > 0 of A128570 is asymptotic to 2^(2*r) * n^r * A128318(n) / (3^r * r!). - Vaclav Kotesovec, Mar 19 2016

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Crossrefs

Cf. A128570 (triangle), other rows: A128318, A128571, A128572, A128573, A128574, A128575; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).

Programs

PARI

{a(n)=local(A=1+(n+7)*x);for(j=0,n,A=1+(n+7-j)*x*A^2 +x*O(x^n)); polcoeff(A,n)}

Formula

G.f.: A(x) = 1 + 7x*R(x,7)^2, where R(x,7) = 1 + 8*x*R(x,8)^2, R(x,8) = 1 + 9*x*R(x,9)^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) ~ 256*n^6*A128318(n)/32805. - Vaclav Kotesovec, Mar 19 2016