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A344050 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*|Lah(n, k)|. Inverse binomial convolution of the unsigned Lah numbers A271703. 2
1, 1, -3, 1, 73, -699, 3001, 24697, -783999, 10946233, -80958779, -656003919, 40097528857, -944102982419, 14449693290033, -81180376526759, -4110744092532479, 203618771909117937, -5868277577182238579, 117997016943575159713, -1055340561026036009559, -45279878749358024400299 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = (-1)^(n-1)*n*n!*hypergeom([1 - n, 1 - n], [2, 2], -1) for n >= 1.

MAPLE

aList := proc(len) local lah;

lah := (n, k) -> `if`(n = k, 1, binomial(n-1, k-1)*n!/k!):

seq(add((-1)^(n-k)*binomial(n, k)*lah(n, k), k = 0..n), n = 0..len-1) end:

print( aList(22) );

MATHEMATICA

a[n_] := (-1)^(n-1) n n! HypergeometricPFQ[{1 - n, 1 - n}, {2, 2}, -1]; a[0] := 1;

Table[a[n], {n, 0, 20}]

CROSSREFS

Cf. A271703, A111596, A344050.

Sequence in context: A082525 A162221 A213127 * A213069 A266277 A016482

Adjacent sequences: A344047 A344048 A344049 * A344051 A344052 A344053

KEYWORD

sign

AUTHOR

Peter Luschny, May 10 2021

STATUS

approved

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Last modified November 29 08:40 EST 2022. Contains 358422 sequences. (Running on oeis4.)