A264928 G.f.: exp( Sum_{n>=1} x^n/n * (1 - 3*x^n)/(1 - x^n) ).

1, 1, -1, -3, -4, -2, 1, 5, 8, 8, 6, 2, -4, -10, -13, -15, -14, -10, -3, 5, 12, 18, 23, 25, 23, 17, 9, 1, -9, -19, -28, -34, -37, -35, -30, -24, -15, -3, 10, 24, 35, 43, 48, 50, 50, 46, 38, 26, 12, -4, -20, -34, -45, -55, -64, -70, -71, -67, -58, -46, -31, -15, 2, 18, 35, 53, 68, 80, 89, 93, 91, 85, 75, 63, 49, 33, 15, -7, -31, -53, -72, -88, -101, -109, -114, -114, -111, -105, -96, -82, -63

Offset

0,4

Links

Paul D. Hanna, Table of n, a(n) for n = 0..5000

Formula

G.f.: ( Product_{n>=1} 1 - x^n )^2 / (1-x)^3.

Example

G.f.: A(x) = 1 + x - x^2 - 3*x^3 - 4*x^4 - 2*x^5 + x^6 + 5*x^7 + 8*x^8 + 8*x^9 + 6*x^10 + 2*x^11 - 4*x^12 - 10*x^13 - 13*x^14 - 15*x^15 +...
where
log(A(x)) = x*(1-3*x)/(1-x) + x^2/2*(1-3*x^2)/(1-x^2) + x^3/3*(1-3*x^3)/(1-x^3) + x^4/4*(1-3*x^4)/(1-x^4) + x^5/5*(1-3*x^5)/(1-x^5) +...
Also,
A(x)*(1-x)^3 = (1-x)^2 * (1-x^2)^2 * (1-x^3)^2 * (1-x^4)^2 * (1-x^5)^3 *...

Prog

(PARI) {a(n) = my(A=1); A = exp( sum(k=1, n+1, (x^k*(1 - 3*x^k)/(1 - x^k)) /k +x*O(x^n) ) ); polcoeff(A, n)}
for(n=0, 120, print1(a(n), ", "))

Crossrefs

Sequence in context: A136374 A303869 A081246 * A323874 A326765 A096411

Adjacent sequences: A264925 A264926 A264927 * A264929 A264930 A264931

Keyword

sign,look

Author

Paul D. Hanna, Dec 14 2015

Status

approved