A377107 G.f.: Sum_{k>=1} x^(7*k-1) * Product_{j=1..k-1} (1-x^(6*k+j-1))/(1-x^j).

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 3, 4, 5, 6, 7, 9, 10, 12, 14, 17, 19, 23, 26, 30, 33, 38, 43, 50, 56, 65, 74, 86, 97, 113, 128, 148, 167, 191, 215, 246, 276, 314, 354, 402, 452, 513, 577, 654, 735, 830, 932, 1052, 1178

Offset: 0

Author

Vaclav Kotesovec, Oct 16 2024

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Column 6 of A350879.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(7*k-1)*Product[(1-x^(6*k+j-1))/(1-x^j), {j, 1, k-1}], {k, 1, nmax/7+1}], {x, 0, nmax}], x]
nmax = 100; p=x^5; s=x^5; Do[p=Normal[Series[p*x^7*(1-x^(7*k-1))*(1-x^(7*k))*(1-x^(7*k+1))*(1-x^(7*k+2))*(1-x^(7*k+3))*(1-x^(7*k+4))*(1-x^(7*k+5))/((1-x^(6*k+5))*(1-x^(6*k+4))*(1-x^(6*k+3))*(1-x^(6*k+2))*(1-x^(6*k+1))*(1-x^(6*k))*(1-x^k)), {x, 0, nmax}]]; s+=p;, {k, 1, nmax/7+1}]; Join[{0}, Take[CoefficientList[s, x], nmax]]

Formula

a(n) ~ 5 * Pi^6 * exp(Pi*sqrt(2*n/3)) / (2 * 3^(3/2) * n^4).