A326559 G.f. A(x) satisfies: Sum_{n>=0} A(x^n)^n = x.

1, 0, 0, -1, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, -2, 0, 3, 0, 2, 0, -4, 0, 0, -1, -2, -3, 8, 0, 0, 0, 0, 3, 4, 0, -7, 0, -2, 0, -9, 0, -10, 0, 6, 12, 8, 0, 8, -1, -4, 3, -2, 0, 16, -10, -6, -3, -14, 0, -21, 0, -14, -24, 50, 5, -3, 0, 4, 6, -1, 0, 28, 0, 48, 12, -68, 0, -17, 0, -20, 3, 14, 0, 36, 35, 10, -3, -38, 0, -34, -21, -52, -54, -16, 30, -46, 0, -22, 75, 171, 0, -28, 0, 6, 27, 6, 0, -6, 0, 19, 39, -75, 0, 79, -40, -28, -132, 24, 0, 267, -1, 30, -111, -252, -55, 5, 0, -198, -3, 46, 0, -81, 49, -42, -32, 528, 0, -150, 0, 656, 114, 26, 0, -433, -145, 150, -63, -514, 0, 160, 0

Offset

1,10

Links

Paul D. Hanna, Table of n, a(n) for n = 1..1300

Formula

a(p^2) = -1 for prime p.

Example

G.f.: A(x) = x - x^4 - x^9 + 2*x^10 - 2*x^16 + 3*x^18 + 2*x^20 - 4*x^22 - x^25 - 2*x^26 - 3*x^27 + 8*x^28 + 3*x^33 + 4*x^34 - 7*x^36 - 2*x^38 - 9*x^40 - 10*x^42 + 6*x^44 + 12*x^45 + 8*x^46 + 8*x^48 - x^49 - 4*x^50 + 3*x^51 - 2*x^52 + 16*x^54 - 10*x^55 - 6*x^56 - 3*x^57 - 14*x^58 - 21*x^60 - 14*x^62 - 24*x^63 + 50*x^64 + 5*x^65 - 3*x^66 + 4*x^68 + 6*x^69 - x^70 + 28*x^72 + 48*x^74 + 12*x^75 - 68*x^76 - 17*x^78 - 20*x^80 + 3*x^81 + ...
such that
x = A(x) + A(x^2)^2 + A(x^3)^3 + A(x^4)^4 + A(x^5)^5 + A(x^6)^6 + A(x^7)^7 + ...
TERMS AT SQUARE POSITIONS.
The terms a(n^2), for n >= 1 , begin:
[1, -1, -1, -2, -1, -7, -1, 50, 3, 171, -1, -433, -1, -1819, -493, -14972, -1, 60377, -1, -184172, -76687, 222858, -1, -374277, 208165, -4443338, 5349603, 75176806, -1, -43902199, -1, -1265783512, 691705812, 1753345623, -1500409643, -5035835610, ...].

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n,
A=concat(A, 0); A[#A] = -polcoeff( sum(m=1, sqrtint(#A)+1, subst(x*Ser(A), x, x^m)^m ), #A); ); A[n]}
for(n=1, 121, print1(a(n), ", "))

Crossrefs

Sequence in context: A065205 A036272 A257403 * A083339 A216278 A133827

Adjacent sequences: A326556 A326557 A326558 * A326560 A326561 A326562

Keyword

sign

Author

Paul D. Hanna, Jul 14 2019

Status

approved