Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

The Function v M m (s;a;z) and Some Well-Known Sequences

Alexsandar Petojevic

Aleja Marsala Tita 4/2
24000 Subotica

Abstract: In this paper we define the function _vM_m(s;a,z), and we study the special cases _1M_m(s;a,z) and _nM_{-1}(1;1,n+1). We prove some new equivalents of Kurepa's hypothesis for the left factorial. Also, we present a generalization of the alternating factorial numbers.

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(Concerned with sequences A000142 A003422 A005165 A000217 A014144 A007489 A000292 A000332 A003389 A014145 A000166 A000125 A000217 A000389 A055795 A027660 A055796 A055797 A032179 A032031 A001710 A001715 A001720 A001725 A066318 A000165 A047053 A014297 A052169 A051398 A051403 A002467 A002720 A000522 .)

Received March 21, 2002; revised version received August 14, 2002. Published in Journal of Integer Sequences August 31, 2002.

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