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A329258 Expansion of e.g.f. -log(1 - Sum_{k>=1} x^(k*(k + 1)/2) / (k*(k + 1)/2)!). 1
0, 1, 1, 3, 10, 44, 251, 1707, 13496, 122108, 1243201, 14060771, 174932274, 2374268974, 34910039164, 552782630401, 9378254813944, 169714311278784, 3263200704705648, 66434349885323328, 1427653109477475098, 32294539445483981821, 767051977023372086530 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(0) = 0; a(n) = A010054(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * A010054(n-k) * k * a(k).

MATHEMATICA

nmax = 22; CoefficientList[Series[-Log[1 - Sum[x^(k (k + 1)/2)/(k (k + 1)/2)!, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

a[n_] := a[n] = Boole[IntegerQ[(8 n + 1)^(1/2)]] + Sum[Binomial[n, k] Boole[IntegerQ[(8 (n - k) + 1)^(1/2)]] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 22}]

CROSSREFS

Cf. A000629, A010054, A205803, A329259.

Sequence in context: A333018 A259352 A205803 * A009648 A007125 A247053

Adjacent sequences:  A329255 A329256 A329257 * A329259 A329260 A329261

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 09 2019

STATUS

approved

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Last modified June 12 22:22 EDT 2021. Contains 344972 sequences. (Running on oeis4.)