OFFSET
0,2
COMMENTS
Definition of poly-Cauchy numbers in A222627.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
Takao Komatsu, Poly-Cauchy numbers, RIMS Kokyuroku 1806 (2012)
Takao Komatsu, Poly-Cauchy numbers with a q parameter, Ramanujan J. 31 (2013), 353-371.
Takao Komatsu, Poly-Cauchy numbers, Kyushu J. Math. 67 (2013), 143-153.
Takao Komatsu, Some recurrence relations of poly-Cauchy numbers, J. Nonlinear Sci. Appl., (2019) Vol. 12, Issue 12, 829-845.
M. Z. Spivey,Combinatorial sums and finite differences, Discr. Math. 307 (24) (2007) 3130-3146.
Wikipedia, Stirling transform
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n,k)*(k+1)^3.
E.g.f.: (1 + x) * (1 + 7 * log(1 + x) + 6 * log(1 + x)^2 + log(1 + x)^3). - Ilya Gutkovskiy, Aug 10 2021
MATHEMATICA
Table[Sum[StirlingS1[n, k] (k + 1)^3, {k, 0, n}], {n, 0, 25}]
PROG
(Magma) [&+[StirlingFirst(n, k)*(k+1)^3: k in [0..n]]: n in [0..25]]; // Bruno Berselli, Mar 28 2013
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*(k+1)^3); \\ Michel Marcus, Nov 14 2015
CROSSREFS
KEYWORD
sign
AUTHOR
Takao Komatsu, Mar 28 2013
STATUS
approved