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A317278 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n-1,k-1)*k^n*n!/k!. 2
1, 1, 2, -15, -164, 4245, 46386, -4901939, 39141656, 11707820361, -671114863610, -29398709945319, 7385525824325364, -307076643365636963, -73748845974115224262, 14299745046516639280005, -237996466462017367478864, -377740669670216316717155055, 75515477307532501838072029326 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the n-th term of the inverse Lah transform of the n-th powers.

LINKS

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

N. J. A. Sloane, Transforms

FORMULA

a(n) = n! * [x^n] Sum_{k>=0} k^n*(x/(1 + x))^k/k!.

MATHEMATICA

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

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

CROSSREFS

Cf. A111884, A256467, A317277, A317279.

Sequence in context: A268070 A204679 A259608 * A140809 A153852 A177396

Adjacent sequences:  A317275 A317276 A317277 * A317279 A317280 A317281

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Jul 25 2018

STATUS

approved

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Last modified May 23 19:07 EDT 2019. Contains 323528 sequences. (Running on oeis4.)