The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360175 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A360175

a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!) * [x^n] (1 - exp(-LambertW(x*exp(-x))))^k.
(history; published version)

#5 by Michael De Vlieger at Sun Jan 29 21:02:30 EST 2023

STATUS

proposed

approved

#4 by Peter Luschny at Sun Jan 29 10:53:39 EST 2023

STATUS

editing

proposed

#3 by Peter Luschny at Sun Jan 29 10:50:20 EST 2023

FORMULA

a(n) = Sum_{k=0..n} |A360176(n, k)|.

CROSSREFS

Cf. A360176.

#2 by Peter Luschny at Sun Jan 29 10:44:51 EST 2023

NAME

allocated for Peter Luschny

a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!) * [x^n] (1 - exp(-LambertW(x*exp(-x))))^k.

DATA

1, 1, 6, 53, 647, 10092, 191915, 4309769, 111682044, 3281731611, 107860953795, 3921762633846, 156322429050397, 6779458454252941, 317841794915501862, 16020304439710056785, 863955306007083830051, 49641711131738762890764, 3027776406780183894833791, 195382900651186641677702197

OFFSET

0,3

MAPLE

egf := k -> (1 - exp(-LambertW(x*exp(-x))))^k / k!:

ser := k -> series(egf(k), x, 22):

T := (n, k) -> (-1)^(n-k)*n!*coeff(ser(k), x, n):

seq(add(T(n, k), k = 0..n), n = 0..19);

KEYWORD

allocated

nonn

AUTHOR

Peter Luschny, Jan 29 2023

STATUS

approved

editing

#1 by Peter Luschny at Sat Jan 28 14:10:48 EST 2023

NAME

allocated for Peter Luschny

KEYWORD

allocated

STATUS

approved