A172440 G.f. satisfies: [x^n] A(x)^((n+1)^2) = (n+1)^2 for n>=1; that is, the coefficient of x^n in the (n+1)^2 power of g.f. A(x) equals (n+1)^2.

1, 1, -3, 11, -49, 134, -1915, -30437, -1176925, -47572678, -2240962254, -119077789557, -7053073003902, -460586576005843, -32870527083358387, -2544978866143616029, -212452025172991768237, -19021387591827001945347

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Example

G.f.: A(x) = 1 + x - 3*x^2 + 11*x^3 - 49*x^4 + 134*x^5 - 1915*x^6 +...
Coefficients in the squared powers of A(x) begin:
A(x)^1: [(1), 1, -3, 11, -49, 134, -1915, -30437, ...];
A(x)^4: [1, (4), -6, 12, -45, -220, -4952, -148944, ...];
A(x)^9: [1, 9, (9), -33, 45, -1044, -13353, -387675, ...];
A(x)^16: [1, 16, 72, (16), -284, -1408, -36152, -857136, ...];
A(x)^25: [1, 25, 225, 775, (25), -6520, -78725, -1861575, ...];
A(x)^36: [1, 36, 522, 3756, 12411, (36), -229128, -4096368, ...];
A(x)^49: [1, 49, 1029, 11907, 80115, 283514, (49), -10015593, ...];
A(x)^64: [1, 64, 1824, 30272, 319760, 2177792, 8628896, (64), ...]; ...
where the coefficients [x^n] A(x)^((n+1)^2) form the squares.

Prog

(PARI) {a(n)=local(A=[1, 1]); for(m=3, n+1, A=concat(A, 0); A[ #A]=(m^2-Vec(Ser(A)^(m^2))[m])/m^2); A[n+1]}

Crossrefs

Sequence in context: A111680 A095822 A025539 * A254536 A333514 A268414

Adjacent sequences: A172437 A172438 A172439 * A172441 A172442 A172443

Keyword

sign

Author

Paul D. Hanna, Feb 02 2010

Status

approved