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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

Alois P. Heinz, Table of n, a(n) for n = 0..22

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);

CROSSREFS

Column sums of A219272.

Partial sums of A219275.

Sequence in context: A129951 A127298 A275255 * A000133 A059086 A215168

Adjacent sequences:  A219270 A219271 A219272 * A219274 A219275 A219276

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 17 2012

STATUS

approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)