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A334193 a(0) = 1; thereafter a(n) = exp(1/n) * Sum_{k>=0} (n*k + 1)^n / ((-n)^k * k!). 2
1, 0, -2, -9, -16, 625, 21384, 571438, 13471744, 188661555, -9794500000, -1476328587789, -134710712340480, -10664210861777200, -744650964057237888, -37832162051689453125, 831929248561267474432, 725944099523076464203157, 167435684777981700601449984 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (-x/(1 - x))^k / Product_{j=1..k} (1 - n*j*x/(1 - x)).

a(n) = n! * [x^n] exp(x + (1 - exp(n*x)) / n), for n > 0.

a(n) = A334192(n,n).

MATHEMATICA

Table[SeriesCoefficient[1/(1 - x) Sum[(-x/(1 - x))^k/Product[(1 - n j x/(1 - x)), {j, 1, k}], {k, 0, n}], {x, 0, n}], {n, 0, 18}]

Join[{1}, Table[n! SeriesCoefficient[Exp[x + (1 - Exp[n x])/n], {x, 0, n}], {n, 1, 18}]]

Join[{1}, Table[Sum[Binomial[n, k]*n^k*BellB[k, -1/n], {k, 0, n}], {n, 1, 18}]] (* Vaclav Kotesovec, Apr 18 2020 *)

CROSSREFS

Cf. A318183, A334162, A334190, A334191, A334192.

Sequence in context: A204424 A062981 A069622 * A200944 A137189 A028503

Adjacent sequences:  A334190 A334191 A334192 * A334194 A334195 A334196

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 18 2020

STATUS

approved

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Last modified May 17 06:30 EDT 2021. Contains 343965 sequences. (Running on oeis4.)