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A219275
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Number of standard Young tableaux for partitions of nonnegative integers into distinct parts with largest part n.
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3
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1, 1, 3, 25, 1069, 368168, 1299366501, 55208013380403, 32401197537296758130, 297072961835477978342245712, 47538199827835784548062928051198402, 146779873623344672821145371965795071455181183, 9581411392319396646028223743176779937161862866453789852
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(2) = 3:
+------+ +------+ +------+
| 1 2 | | 1 3 | | 1 2 |
| 3 .--+ | 2 .--+ +------+
+---+ +---+
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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:
b:= (n, l)-> `if`(n<1, h(l), b(n-1, l) +b(n-1, [l[], n])):
a:= n-> `if`(n=0, 1, b(n-1, [n])):
seq(a(n), n=0..12);
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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}]];
b[n_, l_] := If[n < 1, h[l], b[n - 1, l] + b[n - 1, Append[l, n]]];
a[n_] := If[n == 0, 1, b[n - 1, {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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