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A219273
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Number of standard Young tableaux for all partitions of nonnegative integers into distinct parts with largest part <= n.
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3
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1, 2, 5, 30, 1099, 369267, 1299735768, 55209313116171, 32401252746609874301, 297072994236730724952120013, 47538200124908778784793653003318415, 146779873670882872946054150750588724458499598, 9581411392466176519699106616122834087912451590912289450
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OFFSET
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0,2
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LINKS
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EXAMPLE
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a(2) = 5:
+------+ +------+ +------+ +---+ +-+
| 1 2 | | 1 3 | | 1 2 | | 1 | +-+
| 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-> b(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_] := b[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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