A307596 G.f. A(x) satisfies: A(x) = (1/(1 + x)) * A(x^2)*A(x^3)*A(x^4)* ... *A(x^k)* ...

1, -1, 0, -1, 0, 0, -1, 2, -1, 2, 0, 3, -4, 5, -1, 1, -3, 0, -1, -4, -1, -2, 3, -12, 6, -14, 15, -8, 17, -16, 25, -18, 23, 0, 5, 4, 15, 3, -12, 29, -29, 41, -59, 54, -56, 5, -89, 68, -110, 84, -137, 55, -52, 55, -95, 104, -53, -9, 47, -11, 109, -25, 157, -139, 278, -144, 455, -359, 413, -289, 554

Offset

0,8

Comments

Convolution inverse of A129373.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Formula

G.f.: Product_{k>=1} 1/(1 + x^k)^A074206(k).

Example

G.f.: A(x) = 1 - x - x^3 - x^6 + 2*x^7 - x^8 + 2*x^9 + 3*x^11 - 4*x^12 + 5*x^13 - x^14 + ...

Mathematica

terms = 70; A[_] = 1; Do[A[x_] = 1/(1 + x) Product[A[x^k], {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A074206, A129373, A129374, A318767, A321317.

Sequence in context: A138498 A379016 A276669 * A374354 A373043 A240205

Adjacent sequences: A307593 A307594 A307595 * A307597 A307598 A307599

Keyword

sign

Author

Ilya Gutkovskiy, Apr 17 2019

Status

approved