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A298373 a(n) = n! * [x^n] exp(n*x - exp(x) + 1). 1
1, 0, 0, 1, 17, 273, 4779, 93532, 2047730, 49854795, 1339872113, 39462731031, 1265248227869, 43895994373580, 1639148060192408, 65568985769784897, 2797922570156143597, 126880981472647625557, 6094210606862471240855, 309087628703330034215088, 16508178701980033054460042 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..20.

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k)*n^(n-k)*A000587(k).

MATHEMATICA

Table[n! SeriesCoefficient[Exp[n x - Exp[x] + 1], {x, 0, n}], {n, 0, 20}]

Join[{1}, Table[Sum[Binomial[n, k] n^(n - k) BellB[k, -1] , {k, 0, n}], {n, 1, 20}]]

CROSSREFS

Cf. A000587, A074051, A134980, A193683, A193684, A196835, A290219.

Sequence in context: A170698 A170736 A131865 * A179093 A029811 A113076

Adjacent sequences:  A298370 A298371 A298372 * A298374 A298375 A298376

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 18 2018

STATUS

approved

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Last modified September 18 17:45 EDT 2019. Contains 327178 sequences. (Running on oeis4.)