A303506 G.f.: Sum_{n>=1} (-1)^(n-1) * x^(n^2)/(1 - x^n)^n.

1, 1, 1, 0, 1, -1, 1, -2, 2, -3, 1, -1, 1, -5, 7, -7, 1, 3, 1, -12, 16, -9, 1, 1, 2, -11, 29, -32, 1, 28, 1, -49, 46, -15, 16, -18, 1, -17, 67, -67, 1, 53, 1, -140, 162, -21, 1, -103, 2, 103, 121, -244, 1, 55, 211, -305, 154, -27, 1, -17, 1, -29, 219, -486, 496, -73, 1, -592, 232, 766, 1, -931, 1, -35, 1278, -852, 211, -529, 1, 322, 327, -39, 1, -1654, 1821, -41, 379, -1492, 1, 750, 925, -1584

Offset

1,8

Links

Table of n, a(n) for n=1..92.

Formula

a(n) = Sum_{d|n} binomial(n/d-1, d-1) * (-1)^(d-1) for n>=1.

Example

G.f.: A(x) = x + x^2 + x^3 + x^5 - x^6 + x^7 - 2*x^8 + 2*x^9 - 3*x^10 + x^11 - x^12 + x^13 - 5*x^14 + 7*x^15 - 7*x^16 + x^17 + 3*x^18 + ...
such that
A(x) = x/(1-x) - x^4/(1-x^2)^2 + x^9/(1-x^3)^3 - x^16/(1-x^4)^4 + x^25/(1-x^5)^5 - x^36/(1-x^6)^6 + x^49/(1-x^7)^7 - x^64/(1-x^8)^8 +...

Prog

(PARI) {a(n) = sumdiv(n, d, binomial(n/d-1, d-1) * (-1)^(d-1) )}
for(n=1, 100, print1(a(n), ", "))

Crossrefs

Cf. A143862, A303340, A217668.

Sequence in context: A367125 A074313 A367438 * A213194 A208970 A213939

Adjacent sequences: A303503 A303504 A303505 * A303507 A303508 A303509

Keyword

sign

Author

Paul D. Hanna, Apr 25 2018

Status

approved