login
A376812
G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^j)^2.
5
1, 1, 2, 2, 2, 3, 5, 5, 5, 7, 8, 10, 13, 14, 16, 19, 21, 25, 29, 33, 40, 45, 50, 57, 64, 72, 81, 93, 104, 117, 134, 148, 165, 185, 204, 227, 253, 280, 310, 345, 381, 422, 469, 514, 567, 625, 685, 753, 825, 903, 990, 1086, 1186, 1297, 1419, 1548, 1692, 1845, 2007
OFFSET
0,3
LINKS
FORMULA
G.f.: Sum_{k>=0} Product_{j=1..k} (1 + x^j)^2 * x^j.
a(n) ~ c * A376815^sqrt(n) / sqrt(n), where c = 1/(4*sqrt(3/2 - 2*sinh(arcsinh(3^(3/2)/2)/3)/sqrt(3))) = 0.27647151570071656262813536...
MATHEMATICA
nmax = 100; CoefficientList[Series[Sum[x^(n*(n+1)/2)*Product[1+x^k, {k, 1, n}]^2, {n, 0, Sqrt[2*nmax]}], {x, 0, nmax}], x]
nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^k)*(1 + x^k)*x^k]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p; , {k, 1, Sqrt[2*nmax]}]; Take[CoefficientList[s, x], nmax + 1]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 05 2024
STATUS
approved