|
%I #7 Mar 19 2016 09:33:48
%S 1,7,112,2464,65520,1991808,67189248,2469837888,97765355520,
%T 4132860197760,185458263419520,8794132843507200,439083652465543680,
%U 23017956568726049280,1263929372436815078400,72550400791147384412160
%N Row 6 of table A128570.
%C 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
%H Vaclav Kotesovec, <a href="/A128576/b128576.txt">Table of n, a(n) for n = 0..350</a>
%F 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.
%F a(n) ~ 256*n^6*A128318(n)/32805. - _Vaclav Kotesovec_, Mar 19 2016
%o (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)}
%Y Cf. A128570 (triangle), other rows: A128318, A128571, A128572, A128573, A128574, A128575; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Mar 11 2007
|
