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A219273 Number of standard Young tableaux for all partitions of nonnegative integers into distinct parts with largest part <= n. 3
1, 2, 5, 30, 1099, 369267, 1299735768, 55209313116171, 32401252746609874301, 297072994236730724952120013, 47538200124908778784793653003318415, 146779873670882872946054150750588724458499598, 9581411392466176519699106616122834087912451590912289450 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Wikipedia, Young tableau
EXAMPLE
a(2) = 5:
+------+ +------+ +------+ +---+ +-+
| 1 2 | | 1 3 | | 1 2 | | 1 | +-+
| 3 .--+ | 2 .--+ +------+ +---+
+---+ +---+
MAPLE
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);
MATHEMATICA
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, {}];
Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Nov 02 2022, after Alois P. Heinz *)
CROSSREFS
Column sums of A219272.
Partial sums of A219275.
Sequence in context: A129951 A127298 A275255 * A000133 A059086 A363243
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 17 2012
STATUS
approved

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Last modified March 3 10:46 EST 2024. Contains 370511 sequences. (Running on oeis4.)