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URL: https://oeis.org/A374977

⇱ A374977 - OEIS

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A374977
a(n) = Sum_{i+j+k+l=n, i,j,k,l >= 1} sigma(i)*sigma(j)*sigma(k)*sigma(l).
4
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
1,5
LINKS
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Jul 26 2024
STATUS
approved