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 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

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