A128573 Row 3 of table A128570.

1, 4, 40, 580, 10560, 226560, 5532960, 150570240, 4501422240, 146351879520, 5135738294400, 193376042294400, 7775407679034240, 332528365742227200, 15073953619379719680, 722117116504240994880, 36458486578829035929600

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, A128572, A128574, A128575, A128576; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).

Programs

PARI

{a(n)=local(A=1+(n+4)*x);for(j=0,n,A=1+(n+4-j)*x*A^2 +x*O(x^n)); polcoeff(A,n)}

Formula

G.f.: A(x) = 1 + 4x*R(x,4)^2, where R(x,4) = 1 + 5*x*R(x,5)^2, R(x,5) = 1 + 6*x*R(x,6)^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) ~ 32*n^3*A128318(n)/81. - Vaclav Kotesovec, Mar 19 2016