A128571 Row 1 of table A128570.

1, 2, 12, 114, 1440, 22368, 409248, 8585088, 202733760, 5317663680, 153345634560, 4821848409600, 164211751261440, 6022162697840640, 236652023784960000, 9921992082873223680, 442138176056374548480, 20869300232695599552000, 1040210006521640127367680, 54600929159270409876879360

Offset: 0

Author

Paul D. Hanna, Mar 11 2007

Keywords

• nonn

Links

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

Crossrefs

Cf. A128570 (triangle), other rows: A128318, A128572, A128573, A128574, A128575, A128576; A128577 (square of row 0), A128578 (main diagonal), A128579 (antidiagonal sums).

Cf. A268652.

Programs

PARI

{a(n)=local(A=1+(n+2)*x);for(j=0,n,A=1+(n+2-j)*x*A^2 +x*O(x^n)); polcoeff(A,n)}
for(n=0,25,print1(a(n),", "))

Formula

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