cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A374977 a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 1} sigma(i)*sigma(j)*sigma(k)*sigma(l).

Original entry on oeis.org

0, 0, 0, 1, 12, 70, 280, 885, 2364, 5586, 12000, 23870, 44660, 79272, 134768, 220565, 349440, 538270, 807840, 1187004, 1706840, 2415150, 3354120, 4601870, 6209612, 8303610, 10935960, 14309640, 18460260, 23708184, 30044000, 37967925, 47368480, 59022432, 72633816
Offset: 1

Views

Author

Chai Wah Wu, Jul 26 2024

Keywords

Crossrefs

Programs

  • Mathematica
    b[n_, k_] := b[n, k] = If[k == 0, If[n == 0, 1, 0], If[k == 1, If[n == 0, 0, DivisorSigma[1, n]], Function[q, Sum[b[j, q]*b[n - j, k - q], {j, 0, n}]][Quotient[k, 2]]]];
    a[n_] := b[n, 4];
    Table[a[n], {n, 1, 35}] (* Jean-François Alcover, Jul 11 2025, after Alois P. Heinz in A319083 *)
  • Python
    from sympy import divisor_sigma
    def A374977(n): return sum((5*divisor_sigma(i+1,3)-(5+6*i)*divisor_sigma(i+1))*(5*divisor_sigma(n-i-1,3)-(5+6*(n-i-2))*divisor_sigma(n-i-1)) for i in range(1,n-2))//144

Formula

4-fold convolution of A000203.
Convolution of A000203 and A374951.
Convolution of A000385 with itself.
a(n) = Sum_{i=1..n-1} A000203(i)*A374951(n-i).
a(n) = Sum_{i=1..n-3} A000385(i)*A000385(n-i-2).
Column k=4 of A319083.
Sum_{k=1..n} a(k) ~ Pi^8 * n^8 / 52254720. - Vaclav Kotesovec, Sep 20 2024