A340823 a(n) = exp(-1) * Sum_{k>=0} (k*(k - n))^n / k!.

1, 1, 3, 5, 124, -2075, 91993, -4709903, 312334595, -25531783799, 2524083665172, -296260739274275, 40667620527027177, -6446882734412545043, 1167717545574222779643, -239452569059443831797303, 55146244227862697483251020, -14163492441645773105212592623

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..260

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * Bell(2*n-k) * (-n)^k.

Mathematica

Table[Exp[-1] Sum[(k (k - n))^n/k!, {k, 0, Infinity}], {n, 0, 17}]
Join[{1}, Table[Sum[Binomial[n, k] BellB[2 n - k] (-n)^k, {k, 0, n}], {n, 1, 17}]]

Prog

(Magma)
A340823:= func< n | (&+[(-n)^j*Binomial(n, j)*Bell(2*n-j): j in [0..n]]) >;
[A340823(n): n in [0..30]]; // G. C. Greubel, Jun 12 2024
(SageMath)
def A340823(n): return sum( binomial(n, k)*bell_number(2*n-k)*(-n)^k for k in range(n+1))
[A340823(n) for n in range(31)] # G. C. Greubel, Jun 12 2024

Crossrefs

Cf. A000110, A020556, A020557, A290219, A334243, A340822.

Sequence in context: A153137 A105526 A070743 * A364545 A245442 A215239

Adjacent sequences: A340820 A340821 A340822 * A340824 A340825 A340826

Keyword

sign

Author

Ilya Gutkovskiy, Jan 22 2021

Status

approved