A377300 G.f.: Sum_{k>=1} k * x^(k*(7*k - 7 + 2)/2) / (1 - x^k).

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Offset: 1

Author

Vaclav Kotesovec, Oct 23 2024

Keywords

• nonn

Comments

In general, for d > 0, if g.f. = Sum_{k>=1} k * x^(k*(d*k - d + 2)/2) / (1 - x^k), then Sum_{k=1..n} a(k) ~ 2^(3/2) * n^(3/2) / (3*sqrt(d)).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Column 7 of A334466.

Programs

Mathematica

Table[Sum[If[n > 7*k*(k-1)/2 && IntegerQ[n/k - 7*(k-1)/2], k, 0], {k, Divisors[2*n]}], {n, 1, 100}]
nmax = 100; Rest[CoefficientList[Series[Sum[k*x^(k*(7*k - 7 + 2)/2)/(1 - x^k), {k, 1, Sqrt[2*nmax/7] + 1}], {x, 0, nmax}], x]]

Formula

Sum_{k=1..n} a(k) ~ 2^(3/2) * n^(3/2) / (3*sqrt(7)).