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A222636 Poly-Cauchy numbers c_n^(-3). 4
1, 8, 19, -1, -10, 48, -234, 1302, -8328, 60672, -497688, 4547448, -45846864, 505862064, -6065584128, 78555965184, -1093053332736, 16264215348480, -257730606190080, 4333624828853760, -77067187081620480, 1445257352902763520, -28505367984508416000 (list; graph; refs; listen; history; text; internal format)
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.

M. Z. Spivey,Combinatorial sums and finite differences, Discr. Math. 307 (24) (2007) 3130-3146

Wikipedia, Stirling transform

FORMULA

a(n) = sum(stirling1(n,k)*(k+1)^3, k=0..n).

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

Sequence in context: A146299 A081968 A076096 * A283264 A294588 A259169

Adjacent sequences:  A222633 A222634 A222635 * A222637 A222638 A222639

KEYWORD

sign

AUTHOR

Takao Komatsu, Mar 28 2013

STATUS

approved

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Last modified November 14 12:21 EST 2019. Contains 329114 sequences. (Running on oeis4.)