A052201 Equivalent of the Kurepa hypothesis for left factorial.

4, 15, 48, 175, 816, 4851, 34960, 292743, 2774040, 29251651, 339184776, 4285584615, 58571107168, 860622082035, 13525670637216, 226358825764711, 4018390654376520, 75413358213752643, 1491684815796629080, 31014754853346045831, 676190458445520562896

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Romeo Mestrovic, Variations of Kurepa's left factorial hypothesis, arXiv preprint arXiv:1312.7037 [math.NT], 2013.

Romeo Mestrovic, The Kurepa-Vandermonde matrices arising from Kurepa's left factorial hypothesis, Filomat 29:10 (2015), 2207-2215; DOI 10.2298/FIL1510207M.

Formula

a(1)=4, a(2)=15, a(3)=48, a(n) = (n+1)*( a(n-1)-a(n-3)) - 3*a(n-2).

a(n) = (n+3)*A051403(n-1). - Mohammed Bouras, Aug 05 2022

Mathematica

nxt[{n_, a_, b_, c_}]:={n+1, b, c, (c-a)(n+2)-3b}; NestList[nxt, {3, 4, 15, 48}, 20][[1;; All, 2]] (* Harvey P. Dale, Jan 30 2026 *)

Crossrefs

Cf. A051403.

Sequence in context: A225976 A093967 A380256 * A320460 A178704 A099167

Adjacent sequences: A052198 A052199 A052200 * A052202 A052203 A052204

Keyword

nonn,easy

Author

Aleksandar Petojevic, Jan 28 2000

Extensions

More terms from James Sellers, Jan 31 2000

Status

approved