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A299786 Expansion of Product_{k>=1} (1 + k^(k-1)*x^k). 1
1, 1, 2, 11, 73, 707, 8547, 127379, 2237804, 45511484, 1049155214, 27060763974, 771662014455, 24109614539775, 818906748562249, 30044648617150066, 1184045057676213763, 49883902402848781573, 2237286132689496359239, 106426356238092171308928, 5352031894869594850387969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n) ~ n^(n-1) * (1 + exp(-1)/n + (2*exp(-2) + 3*exp(-1)/2)/n^2). - Vaclav Kotesovec, Jan 22 2019

MATHEMATICA

nmax = 20; CoefficientList[Series[Product[(1 + k^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1) d^(k - k/d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A265949, A321387, A323634.

Sequence in context: A323842 A049671 A074609 * A199417 A114179 A231556

Adjacent sequences:  A299783 A299784 A299785 * A299787 A299788 A299789

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 21 2019

STATUS

approved

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Last modified August 23 00:59 EDT 2019. Contains 326211 sequences. (Running on oeis4.)