login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A222627 Poly-Cauchy numbers c_n^(-2) (for definition see Comments lines). 9
1, 4, 5, -3, 4, -8, 20, -52, 72, 936, -17568, 238752, -3113280, 41503680, -577877760, 8470414080, -131039838720, 2139954163200, -36854615347200, 668374040678400, -12742107588403200, 254904791591116800, -5341386032640000000, 117034910701793280000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The definition of poly-Cauchy numbers is given in Theorem 1 of the paper Poly-Cauchy numbers (see Links lines).

The poly-Cauchy numbers c_n^k can be expressed in terms of the (unsigned) Stirling numbers of the first kind: c_n^(k) = (-1)^n*sum(abs(stirling1(n,m))*(-1)^m/(m+1)^k, m=0..n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

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)^2, k=0..n).

MATHEMATICA

Table[Sum[StirlingS1[n, k]*(k + 1)^2, {k, 0, n}], {n, 0, 25}]

PROG

(MAGMA) [&+[StirlingFirst(n, k)*(k+1)^2: 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)^2); \\ Michel Marcus, Nov 14 2015

CROSSREFS

Cf. A006233.

Sequence in context: A212711 A069197 A021692 * A107793 A275275 A196402

Adjacent sequences:  A222624 A222625 A222626 * A222628 A222629 A222630

KEYWORD

sign

AUTHOR

Takao Komatsu, Mar 28 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)