A208897 A diagonal of rectangular table A208896: a(n) = A208896(n+1,n).

1, 1, 1, 3, 19, 201, 3106, 64522, 1704795, 55095601, 2115975655, 94466053541, 4818194778101, 276874057979927, 17721751093252740, 1251476983229057488, 96724943665929684251, 8125833302851782601185, 737619034028749204655009, 71975174880203583395021875

Offset: 0

Author

Paul D. Hanna, Mar 03 2012

Keywords

• nonn

Comments

The g.f. of row n, R(n,x), in the rectangular table A208896 satisfies:

(1) R(n,x) = 1 + x*R(n,x)^n * [d/dx x/R(n,x)] for n>=0.

(2) [x^k] R(n,x)^(k-n+1) = [x^k] R(n,x)^(k-n) for k>=2.

The main diagonal in A208896 obeys: A208896(n,n) = 0 for n>=2.

Crossrefs

Cf. A208896, A208898.

Programs

PARI

{a(n)=local(ROW=1+x+x*O(x^n));for(i=0,n,ROW=1+x*ROW^(n+1)*deriv(x/ROW));polcoeff(ROW,n)}
for(n=0,21,print1(a(n),","))