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

%I

%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

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Last modified September 19 17:35 EDT 2021. Contains 347564 sequences. (Running on oeis4.)