A326651 a(n) = Sum_{k>0} k * A326616(k,n).

0, 1, 14, 243, 9692, 865445, 196868202, 122831606807, 219073289264824, 1139077903664789577, 17597009238919048388550, 821444189426979675481201211, 116802449602563244067365434335892, 50816512870344533477388136382624158445

Offset: 0

Author

Alois P. Heinz, Sep 12 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A000203, A024916, A326616, A326617.

Programs

Maple

g:= proc(n) option remember; `if`(n=0, 0, numtheory[sigma](n)+g(n-1)) end:
b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add((t->
      b(n-t, min(n-t, i-1), k)*binomial(k, t))(i*j), j=0..n/i)))
    end:
a:= k-> add(n*add(b(n$2, k-i)*(-1)^i*binomial(k, i), i=0..k), n=k..g(k)):
seq(a(n), n=0..15);

Mathematica

g[n_] := g[n] = If[n == 0, 0, DivisorSigma[1, n] + g[n - 1]];
b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, Sum[With[{t = i*j}, b[n - t, Min[n - t, i - 1], k]*Binomial[k, t]], {j, 0, n/i}]]];
a[k_] := Sum[n*Sum[b[n, n, k - i]*(-1)^i*Binomial[k, i], {i, 0, k}], {n, k, g[k]}];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Mar 24 2022, after Alois P. Heinz *)

Formula

a(n) = Sum_{k=n..A024916(n)} k * A326616(k,n) = Sum_{k=n..A024916(n)} k * A326617(k,n).