A328681 a(n) = Sum_{k=1..n} binomial(n,k) * tau(k) * tau(n - k + 1), where tau = A000005.

1, 6, 20, 55, 142, 322, 779, 1608, 3894, 7370, 18372, 33137, 81512, 149694, 353224, 641461, 1570836, 2684928, 6642915, 11795178, 28133846, 46768200, 125433400, 197654545, 485749918, 893864394, 2066417482, 3385115393, 8975476976, 14384181908, 35478028091, 61940000322

Offset

1,2

Links

Table of n, a(n) for n=1..32.

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

Cf. A000005, A007318, A055507, A160399, A330088.

Sequence in context: A059822 A213589 A152959 * A109903 A323640 A249406

Adjacent sequences: A328678 A328679 A328680 * A328682 A328683 A328684

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 03 2019

Status

approved