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A218433
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Sum of the 6th powers of the numbers of standard Young tableaux over all partitions of n.
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2
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1, 1, 2, 66, 1524, 86100, 19902600, 3965056200, 976304082600, 384973061999400, 347437227718904400, 365434181398477976400, 390696545168036224840800, 475968229571639505471170400, 784642922815221782474131569600, 2070759893211522247088843511422400
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OFFSET
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0,3
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LINKS
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MAPLE
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h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j
+add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
end:
g:= proc(n, i, l) `if`(n=0, h(l)^6, `if`(i<1, 0, g(n, i-1, l)+
`if`(i>n, 0, g(n-i, i, [l[], i]))))
end:
a:= n-> `if`(n=0, 1, g(n, n, [])):
seq(a(n), n=0..20);
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MATHEMATICA
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h[l_] := With[{n = Length[l]}, Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i + 1, n}], {j, 1, l[[i]]}], {i, 1, n}]];
g[n_, i_, l_] := g[n, i, l] = If[n == 0, h[l]^6, If[i < 1, 0, g[n, i - 1, l] + If[i > n, 0, g[n - i, i, Append[l, i]]]]];
a[n_] := If[n == 0, 1, g[n, n, {}]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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