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

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

Offset

0,3

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.

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

Links

Table of n, a(n) for n=0..19.

Formula

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

Example

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

Prog

 (PARI) {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), ", "))

Crossrefs

Cf. A208896, A208897.

Sequence in context: A240956 A038035 A133984 * A108995 A184358 A132843

Adjacent sequences: A208895 A208896 A208897 * A208899 A208900 A208901

Keyword

nonn

Author

Paul D. Hanna, Mar 03 2012

Status

approved