A375002 a(n) = Sum_{i+j+k+m=n, i,j,k,m >= 1} tau(i) * tau(j) * tau(k) * tau(m).

0, 0, 0, 1, 8, 32, 92, 216, 440, 814, 1392, 2244, 3452, 5096, 7292, 10129, 13760, 18284, 23868, 30662, 38820, 48556, 59948, 73424, 88796, 106886, 127052, 150732, 176560, 206920, 239344, 277616, 317516, 365034, 413508, 471637, 529712, 600076, 668708, 753070, 833408

Offset: 1

Author

Seiichi Manyama, Jul 27 2024

Keywords

• nonn

Comments

4-fold convolution of tau (A000005).

Crossrefs

Column k=4 of A320019.

Cf. A000005, A055507.

Programs

PARI

my(N=50, x='x+O('x^N)); concat([0, 0, 0], Vec(sum(k=1, N, x^k/(1-x^k))^4))

Formula

G.f.: ( Sum_{k>=1} x^k/(1 - x^k) )^4.

a(n) = Sum_{i=1..n-3} A055507(i)*A055507(n-2-i). - Chai Wah Wu, Jul 27 2024