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A153278
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Array read by antidiagonals of higher order Fubini numbers.
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7
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1, 1, 3, 1, 4, 13, 1, 5, 23, 75, 1, 6, 36, 175, 541, 1, 7, 52, 342, 1662, 4683, 1, 8, 71, 594, 4048, 18937, 47293, 1, 9, 93, 949, 8444, 57437, 251729, 545835, 1, 10, 118, 1425, 15775, 143783, 950512, 3824282, 7087261, 1, 11, 146, 2040, 27146, 313920, 2854261, 17975438, 65361237, 102247563
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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EXAMPLE
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The table on p.6 of Mezo begins:
===========================================================
F_p,n|n=1|n=2|n=3.|.n=4.|..n=5.|....n=6.|.....n=7.|comment
===========================================================
p=1..|.1.|.3.|.13.|..75.|..541.|...4683.|...47293.|.A000670
p=2..|.1.|.4.|.23.|.175.|.1662.|..18937.|..251729.|.A083355
p=3..|.1.|.5.|.36.|.342.|.4048.|..57437.|..950512.|.A099391
p=4..|.1.|.6.|.52.|.594.|.8444.|.143783.|.2854261.|.A363008
p=5..|.1.|.7.|.71.|.949.|15775.|.313920.|.7279795.|.A363009
===========================================================
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MAPLE
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f:= proc(n) option remember; local k; if n<=1 then 1 else
add(binomial(n, k) *f(n-k), k=1..n) fi
end:
stirtr:= proc(a) proc(n) option remember;
add( a(k) *Stirling2(n, k), k=0..n)
end end:
F:= (p, n)-> (stirtr@@(p-1))(f)(n):
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MATHEMATICA
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f[n_] := f[n] = If[n <= 1, 1, Sum[Binomial[n, k]*f[n-k], {k, 1, n}]];
stirtr[a_] := Module[{g}, g[n_] := g[n] = Sum[a[k]*StirlingS2[n, k], {k, 0, n}]; g];
F[p_, n_] := (Composition @@ Table[stirtr, {p-1}])[f][n];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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