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 A124461 Row 1 of rectangular table A124460; also equals the antidiagonal sums of table A124460. 8

%I #3 Mar 30 2012 18:37:01

%S 1,2,4,9,23,66,210,731,2744,10959,46058,202028,919386,4321837,

%T 20916763,103958935,529512396,2759340117,14690668955,79813438230,

%U 442057104246,2493917931493,14320972817368,83652035642564,496769855224824

%N Row 1 of rectangular table A124460; also equals the antidiagonal sums of table A124460.

%C In table A124460, the o.g.f. of row n, R_n(y), satisfies: R_n(y) = Sum_{k>=0} y^k * R_k(y)^n for n>=0.

%F O.g.f.: A(x) = Sum_{n>=0} x^n*R_n(x) = Sum_{k>=0} x^k/(1 - x*R_k(x)), where R_n(x) is the o.g.f. of row n in table A124460.

%o (PARI) {a(n)=local(m=max(n,1),R=vector(m+1,r,vector(m+1,c,binomial(r+c-2,c-1)))); for(i=0,m,for(r=0,m,R[r+1]=Vec(sum(c=0,m,x^c*Ser(R[c+1])^r+O(x^(m+1))))));R[2][n+1]}

%Y Cf. A124460 (table); other rows: A124462, A124463, A124464, A124465, A124466.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Nov 03 2006

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Last modified December 11 11:25 EST 2023. Contains 367724 sequences. (Running on oeis4.)