A336427 a(0) = 0; a(n) = 1 + (1/n) * Sum_{k=1..n-1} binomial(n,k)^3 * k * a(k).

0, 1, 5, 100, 5357, 597726, 120049592, 39381634818, 19686000625517, 14233714132535146, 14293760060523962630, 19298235276251711246358, 34108177389621376109912120, 77181320123960021972892515094, 219430688163572488543090308547898

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

Sum_{n>=0} a(n) * x^n / (n!)^3 = -log(1 - Sum_{n>=1} x^n / (n!)^3).

Mathematica

a[0] = 0; a[n_] := a[n] = 1 + (1/n) Sum[Binomial[n, k]^3 k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 14}]
nmax = 14; CoefficientList[Series[-Log[1 - Sum[x^k/(k!)^3, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!^3

Crossrefs

Cf. A000629, A102223, A193420.

Sequence in context: A078534 A141120 A123668 * A197200 A090436 A140616

Adjacent sequences: A336424 A336425 A336426 * A336428 A336429 A336430

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 21 2020

Status

approved