A330088 a(n) = Sum_{k=1..n} binomial(n,k) * sigma(k) * sigma(n - k + 1), where sigma = A000203.

1, 9, 43, 155, 511, 1442, 4131, 10323, 28171, 63987, 171667, 369395, 957958, 2047694, 5078963, 10671529, 26542339, 53522031, 132273403, 268623854, 647842889, 1266118858, 3197923083, 6058756355, 14581380971, 29480406552, 68634048862, 131847974143, 323289015466, 611887749996

Offset: 1

Author

Ilya Gutkovskiy, Dec 03 2019

Keywords

• nonn

Crossrefs

Cf. A000203, A000385, A007318, A185003, A328681.

Programs

Magma

[&+[Binomial(n,k)*DivisorSigma(1,k)*DivisorSigma(1,n-k+1):k in [1..n]]:n in [1..30]]; // Marius A. Burtea, Dec 03 2019

Mathematica

Table[Sum[Binomial[n, k] DivisorSigma[1, k] DivisorSigma[1, n - k + 1], {k, 1, n}], {n, 1, 30}]
nmax = 30; CoefficientList[Series[(1/2) D[Sum[DivisorSigma[1, k] x^k/k!, {k, 1, nmax}]^2, x], {x, 0, nmax}], x] Range[0, nmax]! // Rest

PARI

a(n) = sum(k=1, n, binomial(n,k)*sigma(k)*sigma(n-k+1)); \\ Michel Marcus, Dec 05 2019

Formula

E.g.f.: (1/2) * d/dx (Sum_{k>=1} sigma(k) * x^k / k!)^2.