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A250117 G.f. A(x) satisfies: [x^n] A(x)^((n+1)(n+2)/2) = 0 for n>1 with a(0)=1 and a(1)=2.

%I A250117 #5 Nov 24 2014 20:27:18
%S A250117 1,2,-10,84,-868,9872,-121392,1522000,-20885744,249139392,-4898915424,
%T A250117 -6811333312,-4215314380800,-213186664776192,-15944754147807232,
%U A250117 -1207550934725368320,-100056122156079206144,-8876452703027927096320
%N A250117 G.f. A(x) satisfies: [x^n] A(x)^((n+1)(n+2)/2) = 0 for n>1 with a(0)=1 and a(1)=2.
%C A250117 This was formerly A147316, but has been renumbered because of a conflict.
%e A250117 G.f.: A(x) = 1 + 2*x - 10*x^2 + 84*x^3 - 868*x^4 + 9872*x^5 +...
%e A250117 The coefficients in the triangular powers of g.f. A(x) begin:
%e A250117 A^1: [1, 2, -10, 84, -868, 9872, -121392, 1522000, -20885744, ...];
%e A250117 A^3: [1, 6, -18, 140, -1416, 15768, -193960, 2369664, -33862320, ...];
%e A250117 A^6: [1, 12, 0, 64, -828, 9504, -128128, 1447680, -25886016, ...];
%e A250117 A^10:[1, 20, 80, 0, -100, 704, -37440, 83200, -15426800, ...];
%e A250117 A^15:[1, 30, 270, 700, 0, -1944, -28600, -627360, -19260000, ...];
%e A250117 A^21:[1, 42, 630, 4004, 9492, 0, -73696, -1380240, -37310112, ...];
%e A250117 A^28:[1, 56, 1232, 13440, 74984, 189728, 0, -3286016, -76931120, ...];
%e A250117 A^36:[1, 72, 2160, 34944, 329112, 1804896, 5181696, 0, -170026128, ...];
%e A250117 A^45:[1, 90, 3510, 77700, 1073700, 9579168, 54737280, 181761840, 0,...]; ...
%e A250117 Note how the coefficient of x^n in A(x)^((n+1)(n+2)/2) = 0 for n>1.
%o A250117 (PARI) {a(n)=local(A=[1, 2]); for(m=3, n+1, A=concat(A, 0); A[#A]=-Vec(Ser(A)^(m*(m+1)/2))[m]/(m*(m+1)/2)); A[n+1]}
%Y A250117 Cf. A171791.
%K A250117 sign
%O A250117 0,2
%A A250117 _Paul D. Hanna_, Feb 05 2011