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A215570
Number of permutations of n indistinguishable copies of 1..5 with every partial sum <= the same partial sum averaged over all permutations.
2
1, 35, 18720, 19369350, 27032968200, 44776592395920, 82881380383401600, 165850226337286576800, 351597937025844947295000, 779279938350147159519336600, 1789294251011628021153241548800, 4228135363283244543270651711564000, 10232120200642411474243152429724152000
OFFSET
0,2
LINKS
Manuel Kauers and Christoph Koutschan, Table of n, a(n) for n = 0..50 (terms 0..47 from Vaclav Kotesovec).
M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023.
FORMULA
a(n) ~ (3*sqrt(5)-5) * 5^(5*n) / (8*Pi^2*n^3). - Vaclav Kotesovec, Sep 06 2016
Conjectured recurrence of order 3 and degree 15: 3*(n + 1)*(n + 2)^3*(n + 4)^2*(3*n + 8)*(3*n + 10)*(65*n^3 + 398*n^2 + 781*n + 496)*(n + 3)^4*a(n + 3) - 20*(n + 1)*(n + 2)^3*(5*n + 11)*(5*n + 12)*(5*n + 13)*(5*n + 14)*(910*n^5 + 11032*n^4 + 52047*n^3 + 119686*n^2 + 134365*n + 58980)*(n + 3)^2*a(n + 2) + 25*(n + 1)*(n + 2)*(5*n + 6)*(5*n + 7)*(5*n + 8)*(5*n + 9)*(5*n + 11)*(5*n + 12)*(5*n + 13)*(5*n + 14)*(2015*n^5 + 24428*n^4 + 114387*n^3 + 258294*n^2 + 281088*n + 118368)*a(n + 1) - 250*(5*n + 1)*(5*n + 2)*(5*n + 3)*(5*n + 4)*(5*n + 6)*(5*n + 7)*(5*n + 8)*(5*n + 9)*(5*n + 11)*(5*n + 12)*(5*n + 13)*(5*n + 14)*(65*n^3 + 593*n^2 + 1772*n + 1740)*a(n) = 0. - Manuel Kauers and Christoph Koutschan, Mar 02 2023
EXAMPLE
a(1) = 35: (1,2,3,4,5), (1,2,3,5,4), ..., (3,2,1,5,4), (3,2,4,1,5).
MAPLE
b:= proc(l) option remember; local m, n, g;
m, n:= nops(l), add(i, i=l);
g:= add(i*l[i], i=1..m)-(m+1)/2*(n-1);
`if`(n<2, 1, add(`if`(l[i]>0 and i<=g,
b(subsop(i=l[i]-1, l)), 0), i=1..m))
end:
a:= n-> b([n$5]):
seq(a(n), n=0..15);
MATHEMATICA
b[l_] := b[l] = Module[{m, n, g}, {m, n} = {Length[l], Total[l]}; g = Sum[i*l[[i]], {i, 1, m}] - (m + 1)/2*(n - 1); If[n < 2, 1, Sum[If[l[[i]] > 0 && i <= g, b[ReplacePart[l, i -> l[[i]] - 1]], 0], {i, 1, m}]]];
a[k_] := b[Array[k&, 5]];
a /@ Range[0, 15] (* Jean-François Alcover, Dec 18 2020, after Alois P. Heinz *)
CROSSREFS
Row n=5 of A215561.
Sequence in context: A007102 A196542 A271072 * A271073 A271074 A249890
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 16 2012
STATUS
approved