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 A347930 3-Springer numbers. 0
 1, 1, 3, 16, 88, 625, 5527, 55760, 640540, 8329326, 120212331, 1905939913, 32987637967, 618591571085, 12489644875037, 270193806214360, 6235154917414954, 152875655211527878, 3968729594485785289, 108754865309750398187, 3137052120203959610759 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS a(n) is also the volume of a certain flow polytope. LINKS Table of n, a(n) for n=2..22. Arvind Ayyer, Matthieu Josuat-Vergès, and Sanjay Ramassamy, Extensions of partial cyclic orders and consecutive coordinate polytopes, Ann. H. Lebesgue, 3 (2020), 275-297. R. S. Gonzalez D'Leon, A. H. Morales, C. R. H. Hanusa, and M. Yip, Column convex matrices, G-cyclic orders, and flow polytopes, arXiv:2107.07326 [math.CO], 2021. S. Ramassamy, Extensions of partial cyclic orders, Euler numbers and multidimensional boustrophedons, Electron. J. Combin., 25 (2018), #P1.66. FORMULA a(n) = Sum_{(x,y,z), x+y+z=n-2} ((n-2)!/(x!*y!*z!))*b(x,y,z), where b(x,y,z) are the 3-Entringer numbers defined by Ramassamy. MAPLE wcomps:=proc(n, k) option remember; local ocomps, ncomps, i; ocomps:=combinat:-composition(n+k, k); ncomps:={}; for i from 1 to nops(ocomps) do ncomps:=ncomps union{[seq(ocomps[i][j]-1, j=1..k)]}; end do; return [op(ncomps)]; end proc: b:=proc(s) option remember; local k; k := nops(s); if s = [seq(0, i=1..k)] then return(1); elif s[1]>0 then return(add(b([s[2]+j, op(s[3..k]), s[1]-j-1]), j=0..s[1]-1)); else return(0); end if; end proc:a:=proc(n) local N, S: N := n-2; S := wcomps(N, 3); return add(combinat:-multinomial(N, op(s))*b(s), s in S); end proc:seq(a(n), n=2..10); CROSSREFS Cf. A001586, A008282, A000111. Sequence in context: A163604 A151329 A356402 * A026111 A026330 A146963 Adjacent sequences: A347927 A347928 A347929 * A347931 A347932 A347933 KEYWORD nonn AUTHOR Alejandro H. Morales, Sep 19 2021 STATUS approved

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Last modified July 24 01:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)