|
%I #7 May 07 2014 01:59:40
%S 1,1,-3,20,-245,4290,-114422,4086800,-203647509,12920587070,
%T -1053926397590,105178069321944,-12765014959365682,
%U 1838898931467398164,-311221726754896488780,61047560951879121055296,-13747598006865584455353165,3521759025274977423306328182,-1018406456608128511401443183654
%N G.f. satisfies: [x^n] A(x)^(n^2) = [x^n] A(x)^(n^2-1) for n>1 with A(0)=A'(0)=1.
%H Paul D. Hanna, <a href="/A237652/b237652.txt">Table of n, a(n) for n = 0..150</a>
%e G.f.: A(x) = 1 + x - 3*x^2 + 20*x^3 - 245*x^4 + 4290*x^5 - 114422*x^6 +...
%e The coefficients in relevant powers of g.f. A(x) begin:
%e A^3: [1, 3, (-6), 43, -597, 11127, -313038, 11486268, ...];
%e A^4: [1, 4, (-6), 48, -721, 13836, -399342, 14835168, ...];
%e ...
%e A^8: [1, 8, 4, (48), -1022, 21328, -677040, 26240352, ...];
%e A^9: [1, 9, 9, (48), -1071, 22572, -732768, 28655712, ...];
%e ...
%e A^15: [1, 15, 60, 125, (-1260), 26508, -986720, 40214775, ...];
%e A^16: [1, 16, 72, 160, (-1260), 26688, -1018704, 41720576, ...];
%e ...
%e A^24: [1, 24, 204, 848, 54, (25680), -1211936, 50397024, ...];
%e A^25: [1, 25, 225, 1000, 525, (25680), -1230900, 51117200, ...];
%e ...
%e A^35: [1, 35, 490, 3675, 14035, 52927, (-1360590), 54736260, ...];
%e A^36: [1, 36, 522, 4080, 16695, 61452, (-1360590), 54781344, ...];
%e ...
%e A^48: [1, 48, 984, 11488, 82428, 399936, -450096, (53190144), ...];
%e A^49: [1, 49, 1029, 12348, 91679, 460110, -217266, (53190144), ...];
%e ...
%e which illustrates [x^n] A(x)^(n^2-1) = [x^n] A(x)^(n^2) for n>1.
%o (PARI) {a(n)=local(A=[1, 1]); for(i=2, n, A=concat(A, 0); A[ #A]=(Vec(Ser(A)^((#A-1)^2-1))-Vec(Ser(A)^((#A-1)^2)))[ #A]); A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A158882, A171791.
%K sign
%O 0,3
%A _Paul D. Hanna_, May 07 2014
|
