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A330605
a(n) = exp(-1) * Sum_{k>=0} (n*k - 1)^n / k!.
5
1, 0, 5, 89, 2737, 121399, 7316101, 572218716, 56142822849, 6731180810945, 965898950508901, 163116461798211503, 31969444766902475185, 7187057932197297484108, 1834860441330563739401765, 527403671798720265634312349, 169396494914472404237224898305
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OFFSET
0,3
LINKS
Table of n, a(n) for n=0..16.
FORMULA
a(n) = n! * [x^n] exp(exp(n*x) - x - 1).
a(n) = Sum_{k=0..n} (-1)^(n - k) * binomial(n,k) * n^k * Bell(k).
MATHEMATICA
Table[Exp[-1] Sum[(n k - 1)^n/k!, {k, 0, Infinity}], {n, 0, 16}]
Join[{1}, Table[Sum[(-1)^(n - k) Binomial[n, k] n^k BellB[k], {k, 0, n}], {n, 1, 16}]]
Table[n! SeriesCoefficient[Exp[Exp[n x] - x - 1], {x, 0, n}], {n, 0, 16}]
CROSSREFS
Cf.
A000110
,
A000296
,
A124311
,
A292914
,
A307066
,
A330604
.
Sequence in context:
A134497
A358388
A339001
*
A028353
A191512
A015085
Adjacent sequences:
A330602
A330603
A330604
*
A330606
A330607
A330608
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy
, Dec 19 2019
STATUS
approved
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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)