OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..6279 (terms 0..250 from Vaclav Kotesovec)
FORMULA
G.f.: 1/(1 - x/(1 - x^2*(1-x)/(1-x^2 - x^3*(1-2*x^2)/(1-2*x^3 - x^4*(1-3*x^3)/(1-3*x^4 - x^5*(1-4*x^4)/(1-4*x^5 -...))))), a continued fraction.
From Vaclav Kotesovec, Jun 18 2019: (Start)
a(n) ~ c * 3^(n/3), where
c = 23.5612420584121380174441491950859168338330954540437... if mod(n,3)=0
c = 23.5209031427848763179214171003561794127717213180726... if mod(n,3)=1
c = 23.5214569018665529984420312927586688667133017590049... if mod(n,3)=2
(End)
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 2*x^4 + 4*x^5 + 5*x^6 + 9*x^7 + 11*x^8 +...
where A(x) = 1 + x/(1-x) + x^3/((1-x)*(1-2*x^2)) + x^6/((1-x)*(1-2*x^2)*(1-3*x^3)) + x^10/((1-x)*(1-2*x^2)*(1-3*x^3)*(1-4*x^4)) +...
MATHEMATICA
Table[SeriesCoefficient[Sum[x^Binomial[n + 1, 2]/Product[(1 - k*x^k), {k, 1, n}], {x, 0, 100}], {x, 0, n}], {n, 0, 50}] (* G. C. Greubel, Dec 19 2017 *)
PROG
(PARI) {a(n)=polcoeff(1+sum(m=1, n, x^(m*(m+1)/2)/prod(k=1, m, 1-k*x^k+x*O(x^n))), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 20 2012
STATUS
approved