A222748 Poly-Cauchy numbers c_n^(-4).

1, 16, 65, 45, -116, 340, -1240, 5480, -28464, 169248, -1125840, 8197680, -63806016, 514314240, -4058967744, 26952984000, -37203513984, -4251686488704, 140692872720384, -3560137793538048, 84004474130786304, -1955196907518928896, 45927815909901004800

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)^4.

Mathematica

Table[Sum[StirlingS1[n, k] (k + 1)^4, {k, 0, n}], {n, 0, 25}]

Prog

(Magma) [&+[StirlingFirst(n, k)*(k+1)^4: 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)^4); \\ Michel Marcus, Nov 14 2015

Crossrefs

Sequence in context: A327496 A330824 A189806 * A283271 A031446 A294584

Adjacent sequences: A222745 A222746 A222747 * A222749 A222750 A222751

Keyword

sign

Author

Takao Komatsu, Mar 28 2013

Status

approved