Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Mar 30 2012 18:37:37
%S 1,1,2,9,72,880,14946,331177,9157984,305879724,12036430600,
%T 547226046939,28298540270928,1643380366183920,106042236588594096,
%U 7535372761616117625,585204851983514095424,49344635724104556446660,4491848127809479571999928,439231681095730953672503448
%N A diagonal of rectangular table A208896: a(n) = A208896(n+2,n).
%C The g.f. of row n, R(n,x), in the rectangular table A208896 satisfies:
%C (1) R(n,x) = 1 + x*R(n,x)^n * [d/dx x/R(n,x)] for n>=0.
%C (2) [x^k] R(n,x)^(k-n+1) = [x^k] R(n,x)^(k-n) for k>=2.
%C Thus the main diagonal in A208896 obeys: A208896(n,n) = 0 for n>=2.
%F a(n) is divisible by n for n>=1.
%e a(n)/n = [1,1,3,18,176,2491,47311,1144748,33986636,1203643060,...] for n>=1.
%o (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)}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A208896, A208897.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Mar 03 2012