A298373 a(n) = n! * [x^n] exp(n*x - exp(x) + 1).

1, 0, 0, 1, 17, 273, 4779, 93532, 2047730, 49854795, 1339872113, 39462731031, 1265248227869, 43895994373580, 1639148060192408, 65568985769784897, 2797922570156143597, 126880981472647625557, 6094210606862471240855, 309087628703330034215088, 16508178701980033054460042

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..386

N. J. A. Sloane, Transforms

Formula

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

a(n) ~ exp(1-exp(1)) * n^n. - Vaclav Kotesovec, Aug 04 2021

Maple

b:= proc(n, k) option remember; `if`(n=0, 1,
      k*b(n-1, k)+ b(n-1, k-1))
    end:
a:= n-> abs(b(n, -n)):
seq(a(n), n=0..20);  # Alois P. Heinz, Aug 04 2021

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