OFFSET
1,2
FORMULA
E.g.f.: (1/2) * d/dx (Sum_{k>=1} tau(k) * x^k / k!)^2.
MATHEMATICA
Table[Sum[Binomial[n, k] DivisorSigma[0, k] DivisorSigma[0, n - k + 1], {k, 1, n}], {n, 1, 32}]
nmax = 32; CoefficientList[Series[(1/2) D[Sum[DivisorSigma[0, k] x^k/k!, {k, 1, nmax}]^2, x], {x, 0, nmax}], x] Range[0, nmax]! // Rest
PROG
(Magma) [&+[Binomial(n, k)*DivisorSigma(0, k)*DivisorSigma(0, n-k+1):k in [1..n]]:n in [1..32]]; // Marius A. Burtea, Dec 03 2019
(PARI) a(n) = sum(k=1, n, binomial(n, k)*numdiv(k)*numdiv(n-k+1)); \\ Michel Marcus, Dec 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Dec 03 2019
STATUS
approved