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Second diagonal of triangle A108990, in which the g.f. of row n, R_n(x), satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1.
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%I #4 Mar 30 2012 18:36:46

%S 1,2,9,76,1025,19656,495964,15629720,593136513,26392662280,

%T 1349451117586,78039195326676,5040212158570043,359802563875687310,

%U 28145720807393650140,2395126209579348837776,220346109158340083116065

%N Second diagonal of triangle A108990, in which the g.f. of row n, R_n(x), satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1.

%F a(n) = A108990(n+1, n) for n>=0. a(n) = (n+1)*A108993(n).

%o (PARI) {a(n)=local(F=1+x*O(x^n));for(m=1,n+1,F=(1+x*F)^m);polcoeff(F,n)}

%Y Cf. A108990, A108991, A108993, A108994, A108995, A108996.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jun 15 2005