A223899 Poly-Cauchy numbers of the second kind hat c_n^(-2).

1, -4, 13, -51, 244, -1392, 9260, -70508, 605320, -5788008, 61021872, -703384272, 8801449344, -118828732032, 1721888828928, -26656798602240, 439110126743040, -7669109089082880, 141557837068938240, -2753560001544053760, 56299265625742848000

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Takao Komatsu, Poly-Cauchy numbers with a q parameter, Ramanujan J. 31 (2013), 353-371.

Takao Komatsu, Poly-Cauchy numbers, RIMS Kokyuroku 1806 (2012), p. 42-53.

Takao Komatsu, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143-153.

Formula

E.g.f.: (1 - log(1 + x) * (3 - log(1 + x))) / (1 + x). - Ilya Gutkovskiy, Aug 09 2021

Mathematica

Table[Sum[StirlingS1[n, k] (-1)^k (k + 1)^2, {k, 0, n}], {n, 0, 30}]

Prog

(Magma) [&+[StirlingFirst(n, k)*(-1)^k*(k+1)^2: k in [0..n]]: n in [0..23]]; // Vincenzo Librandi, Aug 03 2013
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*(-1)^k*(k+1)^2); \\ Michel Marcus, Nov 14 2015

Crossrefs

Cf. A222627.

Sequence in context: A149462 A151488 A245156 * A357962 A097169 A149463

Adjacent sequences: A223896 A223897 A223898 * A223900 A223901 A223902

Keyword

sign

Author

Takao Komatsu, Mar 29 2013

Status

approved