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A336427
a(0) = 0; a(n) = 1 + (1/n) * Sum_{k=1..n-1} binomial(n,k)^3 * k * a(k).
1
0, 1, 5, 100, 5357, 597726, 120049592, 39381634818, 19686000625517, 14233714132535146, 14293760060523962630, 19298235276251711246358, 34108177389621376109912120, 77181320123960021972892515094, 219430688163572488543090308547898
OFFSET
0,3
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 21 2020
STATUS
approved