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A302398 a(n) = n! * [x^n] 1/(1 + x*exp(n*x)). 0
1, -1, -2, 3, 248, 5655, 62064, -3516625, -376936064, -21890186577, -495165203200, 96687112380639, 20607024735783936, 2471270260977141767, 142697263160045590528, -25986252776953159328625, -11860424645318274482077696, -2719428501410438623907546529, -372732332273232481973818294272 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = n!*Sum_{k=0..n} (-1)^(n-k)*(n*(n-k))^k/k!.

a(n) = Sum_{k=0..n} (-1)^k*k!*(n*k)^(n-k)*binomial(n,k).

MATHEMATICA

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

Join[{1}, Table[n! Sum[(-1)^(n - k) (n (n - k))^k/k!, {k, 0, n}], {n, 18}]]

Join[{1}, Table[Sum[(-1)^k k! (n k)^(n - k) Binomial[n, k], {k, 0, n}], {n, 18}]]

CROSSREFS

Cf. A134095, A235328, A302397.

Sequence in context: A142960 A117324 A037059 * A087313 A004876 A177505

Adjacent sequences:  A302395 A302396 A302397 * A302399 A302400 A302401

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Apr 07 2018

STATUS

approved

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Last modified February 21 06:40 EST 2019. Contains 320371 sequences. (Running on oeis4.)