A208896 -id:A208896 - cp's OEIS frontend

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

Paul D. Hanna, Mar 03 2012

nonn

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.

Cf. A208896, A208898.

{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),","))

A208898 A diagonal of rectangular table A208896: a(n) = A208896(n+2,n).

Original entry on oeis.org

1, 1, 2, 9, 72, 880, 14946, 331177, 9157984, 305879724, 12036430600, 547226046939, 28298540270928, 1643380366183920, 106042236588594096, 7535372761616117625, 585204851983514095424, 49344635724104556446660, 4491848127809479571999928, 439231681095730953672503448

Offset: 0

Paul D. Hanna, Mar 03 2012

nonn

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

			a(n)/n = [1,1,3,18,176,2491,47311,1144748,33986636,1203643060,...] for n>=1.

Cf. A208896, A208897.

{a(n)=local(ROW=1+x+x*O(x^n));for(i=0,n,ROW=1+x*ROW^(n+2)*deriv(x/ROW));polcoeff(ROW,n)}
for(n=0,20,print1(a(n),", "))

a(n) is divisible by n for n>=1.

cp's OEIS Frontend

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

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