A237652 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.

1, 1, -3, 20, -245, 4290, -114422, 4086800, -203647509, 12920587070, -1053926397590, 105178069321944, -12765014959365682, 1838898931467398164, -311221726754896488780, 61047560951879121055296, -13747598006865584455353165, 3521759025274977423306328182, -1018406456608128511401443183654

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..150

Example

G.f.: A(x) = 1 + x - 3*x^2 + 20*x^3 - 245*x^4 + 4290*x^5 - 114422*x^6 +...
The coefficients in relevant powers of g.f. A(x)  begin:
A^3: [1, 3, (-6), 43, -597, 11127, -313038, 11486268, ...];
A^4: [1, 4, (-6), 48, -721, 13836, -399342, 14835168, ...];
...
A^8: [1, 8,   4, (48), -1022, 21328, -677040, 26240352, ...];
A^9: [1, 9,   9, (48), -1071, 22572, -732768, 28655712, ...];
...
A^15: [1, 15, 60, 125, (-1260), 26508,  -986720, 40214775, ...];
A^16: [1, 16, 72, 160, (-1260), 26688, -1018704, 41720576, ...];
...
A^24: [1, 24, 204,  848,  54, (25680), -1211936, 50397024, ...];
A^25: [1, 25, 225, 1000, 525, (25680), -1230900, 51117200, ...];
...
A^35: [1, 35, 490, 3675, 14035, 52927, (-1360590), 54736260, ...];
A^36: [1, 36, 522, 4080, 16695, 61452, (-1360590), 54781344, ...];
...
A^48: [1, 48,  984, 11488, 82428, 399936, -450096, (53190144), ...];
A^49: [1, 49, 1029, 12348, 91679, 460110, -217266, (53190144), ...];
...
which illustrates [x^n] A(x)^(n^2-1) = [x^n] A(x)^(n^2) for n>1.

Prog

(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]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A158882, A171791.

Sequence in context: A219541 A200527 A237431 * A256018 A227469 A349928

Adjacent sequences: A237649 A237650 A237651 * A237653 A237654 A237655

Keyword

sign

Author

Paul D. Hanna, May 07 2014

Status

approved