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A307080
a(n) = exp(1) * Sum_{k>=0} (-1)^k*(n*k + 1)^n/k!.
2
1, 0, -3, 19, 497, -1899, -489491, -15433676, 618450881, 120846851155, 7012261819901, -467816186167659, -175527285590430863, -20961845760818684812, 568194037748383908653, 898095630359015975379151, 220433074470274983356464897, 16144974747716546214909454181
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OFFSET
0,3
LINKS
Table of n, a(n) for n=0..17.
FORMULA
a(n) = n! * [x^n] exp(1 + x - exp(n*x)).
a(n) = Sum_{k=0..n} binomial(n,k) * n^k *
A000587
(k).
MATHEMATICA
Table[Exp[1] Sum[(-1)^k (n k + 1)^n/k!, {k, 0, Infinity}], {n, 0, 17}]
Table[n! SeriesCoefficient[Exp[1 + x - Exp[n x]], {x, 0, n}], {n, 0, 17}]
Join[{1}, Table[Sum[Binomial[n, k] n^k BellB[k, -1], {k, 0, n}], {n, 1, 17}]]
CROSSREFS
Cf.
A000587
,
A284860
,
A285065
,
A293037
,
A298373
,
A307066
,
A308645
.
Sequence in context:
A176232
A079306
A051381
*
A337528
A136372
A272571
Adjacent sequences:
A307077
A307078
A307079
*
A307081
A307082
A307083
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy
, Jun 24 2019
STATUS
approved
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Last modified August 23 10:54 EDT 2024. Contains 375396 sequences. (Running on oeis4.)