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A206801 a(n) equals the sum of the coefficients of x^(n-1) in A(x)^k as k=1..n, where A(x) = Sum_{n>=0} a(n)*x^n.

%I A206801 #9 Mar 30 2012 18:37:35
%S A206801 1,1,3,22,285,5476,143080,4840256,205348521,10675415800,667749546288,
%T A206801 49499829165414,4292944063388838,430749877491962328,
%U A206801 49520529524763502478,6467220964216618610444,952209872438113961762005,157000879970348439087083080
%N A206801 a(n) equals the sum of the coefficients of x^(n-1) in A(x)^k as k=1..n, where A(x) = Sum_{n>=0} a(n)*x^n.
%F A206801 G.f. A(x) satisfies: a(n) = Sum_{k=1..n} [x^(n-1)] A(x)^k for n>=1, with a(0)=1.
%e A206801 G.f.: A(x) = 1 + x + 3*x^2 + 22*x^3 + 285*x^4 + 5476*x^5 + 143080*x^6 +...
%e A206801 The coefficients in the powers of the g.f. A(x) begin:
%e A206801 A^1: [1, 1,  3,  22,  285,  5476,  143080,  4840256, ...];
%e A206801 A^2: [1, 2,  7,  50,  623, 11654,  299306, 10012068, ...];
%e A206801 A^3: [1, 3, 12,  85, 1023, 18627,  469956, 15539040, ...];
%e A206801 A^4: [1, 4, 18, 128, 1495, 26500,  656450, 21446816, ...];
%e A206801 A^5: [1, 5, 25, 180, 2050, 35391,  860365, 27763280, ...];
%e A206801 A^6: [1, 6, 33, 242, 2700, 45432, 1083451, 34518774, ...];
%e A206801 A^7: [1, 7, 42, 315, 3458, 56770, 1327648, 41746335, ...];
%e A206801 A^8: [1, 8, 52, 400, 4338, 69568, 1595104, 49481952, ...]; ...
%e A206801 where a(n) = sum of the first n coefficients in column n-1 for n>=1:
%e A206801 a(1) = 1,
%e A206801 a(2) = 1 + 2 = 3;
%e A206801 a(3) = 3 + 7 + 12 = 22;
%e A206801 a(4) = 22 + 50 + 85 + 128 = 285;
%e A206801 a(5) = 285 + 623 + 1023 + 1495 + 2050 = 5476; ...
%o A206801 (PARI) {a(n)=local(A=[1]);for(i=1,n,A=concat(A,sum(m=1,#A,Vec(Ser(A)^m)[#A])));A[n+1]}
%o A206801 for(n=0,21,print1(a(n),", "))
%Y A206801 Cf. A088358.
%K A206801 nonn
%O A206801 0,3
%A A206801 _Paul D. Hanna_, Feb 12 2012