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A331336 L.g.f.: log(Sum_{k>=0} k! * x^k / Product_{j=1..k} (1 - x^j)). 1
1, 5, 19, 97, 571, 4109, 33643, 310321, 3167101, 35427605, 430918489, 5663534761, 79999275253, 1208843786897, 19460746819099, 332560305456673, 6012905371554295, 114689550634547009, 2301617124055928731, 48479953395028134577, 1069433968820519576377 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

FORMULA

exp(Sum_{n>=1} a(n) * x^n / n) = g.f. of A101880.

a(n) = n * A101880(n) - Sum_{k=1..n-1} A101880(k) * a(n-k).

a(n) ~ n * n! * (1 - 1/n^2 - 6/n^3 - 38/n^4 - 276/n^5 - 2354/n^6 - 23458/n^7 - 268991/n^8 - 3490842/n^9 - 50520252/n^10 - ...). - Vaclav Kotesovec, Jan 28 2020

MATHEMATICA

nmax = 21; CoefficientList[Series[Log[Sum[k! x^k/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

CROSSREFS

Cf. A000203, A101880.

Sequence in context: A263245 A020050 A106958 * A146144 A162292 A321875

Adjacent sequences:  A331333 A331334 A331335 * A331337 A331338 A331339

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 14 2020

STATUS

approved

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Last modified April 5 13:33 EDT 2020. Contains 333241 sequences. (Running on oeis4.)