A321948 Column k=3 of triangle A257673.

1, 9, 45, 174, 576, 1719, 4761, 12441, 31050, 74593, 173547, 392787, 867876, 1877322, 3984636, 8314434, 17082510, 34604523, 69194309, 136709688, 267111510, 516515227, 989147760, 1877103486, 3531796959, 6591644601, 12208734552, 22449066710, 40995144288

Offset: 3

Author

Alois P. Heinz, Nov 22 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..5000

Crossrefs

Column k=3 of A257673.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, k*add(
      b(n-j, k)*numtheory[sigma][2](j), j=1..n)/n)
    end:
a:= n-> (k-> add(b(n, k-i)*(-1)^i*binomial(k, i), i=0..k))(3):
seq(a(n), n=3..35);

Formula

G.f.: (-1 + Product_{k>=1} 1 / (1 - x^k)^k)^3. - Ilya Gutkovskiy, Jan 30 2021