A224898 G.f.: Sum_{n>=0} (-1)^n* x^(n*(n+1)) / Product_{k=1..n} (1-x^k).

1, 0, -1, -1, -1, -1, 0, 0, 1, 1, 2, 2, 2, 2, 2, 1, 1, 0, -1, -2, -2, -4, -4, -5, -5, -6, -5, -6, -4, -4, -3, -2, 1, 1, 4, 5, 8, 9, 12, 12, 15, 15, 17, 16, 18, 15, 16, 13, 13, 8, 7, 1, 0, -7, -9, -17, -19, -27, -29, -37, -38, -46, -46, -53, -51, -57, -53, -57, -51, -53, -45, -45, -32, -31

Offset

0,11

Comments

Conjecture: a(n+1) = A286744(n) - A286745(n). - George Beck May 13 2017

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Paul D. Hanna)

Example

G.f.: A(x) = 1 - x^2 - x^3 - x^4 - x^5 + x^8 + x^9 + 2*x^10 + 2*x^11 + 2*x^12 + 2*x^13 + 2*x^14 + x^15 + x^16 - x^18 +...
where
A(x) = 1 - x^2/(1-x) + x^6/((1-x)*(1-x^2)) - x^12/((1-x)*(1-x^2)*(1-x^3)) + x^20/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) - x^30/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)) +...

Prog

(PARI) a(n)=polcoeff(sum(m=0, sqrtint(n), (-1)^m*x^(m*(m+1))/prod(k=1, m, 1-x^k, 1+x*O(x^n))), n)
for(n=0, 80, print1(a(n), ", "))

Crossrefs

Cf. A227620, A227543, A039924, A005169, A286744, A286745, A003106.

Sequence in context: A249071 A231713 A340945 * A027360 A037806 A038082

Adjacent sequences: A224895 A224896 A224897 * A224899 A224900 A224901

Keyword

sign,look

Author

Paul D. Hanna, Jul 24 2013

Status

approved