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A223899
Poly-Cauchy numbers of the second kind hat c_n^(-2).
4
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
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
KEYWORD
sign
AUTHOR
Takao Komatsu, Mar 29 2013
STATUS
approved