OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..6263
FORMULA
G.f.: 1/(1 - x/(1 - 2*x^2*(1-x)/(1 - 3*x^3*(1-2*x^2)/(1 - 4*x^4*(1-3*x^3)/(1 - 5*x^5*(1-4*x^4)/(1 - 6*x^6*(1-5*x^5)/(1 -...)))))), a continued fraction.
From Vaclav Kotesovec, Jun 18 2019: (Start)
a(n) ~ c * 3^(n/3), where
c = 8007.60951343849770902289074154120578227939552369... if mod(n,3)=0
c = 8007.30566699919825273673656299755925992856381905... if mod(n,3)=1
c = 8007.19663204881021378993302255541874790731157021... if mod(n,3)=2
(End)
EXAMPLE
G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 3*x^4 + 7*x^5 + 13*x^6 + 21*x^7 +...
where A(x) = 1 + x/(1-x) + 2!*x^3/((1-x)*(1-2*x^2)) + 3!*x^6/((1-x)*(1-2*x^2)*(1-3*x^3)) + 4!*x^10/((1-x)*(1-2*x^2)*(1-3*x^3)*(1-4*x^4)) +...
MATHEMATICA
Table[SeriesCoefficient[Sum[n!*x^Binomial[n + 1, 2]/Product[(1 - k*x^k), {k, 1, n}], {n, 0, 100}], {x, 0, n}], {n, 0, 50}] (* G. C. Greubel, Dec 19 2017 *)
PROG
(PARI) {a(n)=polcoeff(1+sum(m=1, n, m!*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