The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A218437 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A218437

Sum of the 10th powers of the numbers of standard Young tableaux over all partitions of n.
(history; published version)

#12 by Bruno Berselli at Thu May 18 03:23:44 EDT 2017

STATUS

proposed

approved

#11 by Jean-François Alcover at Thu May 18 03:01:12 EDT 2017

STATUS

editing

proposed

#10 by Jean-François Alcover at Thu May 18 03:01:08 EDT 2017

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}]];

g[n_, i_, l_] := g[n, i, l] = If[n == 0, h[l]^10, 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, {}]];

Table[a[n], {n, 0, 20}] (* Jean-François Alcover, May 18 2017, translated from Maple *)

STATUS

approved

editing

#9 by Alois P. Heinz at Wed Feb 08 19:34:09 EST 2017

STATUS

editing

approved

#8 by Alois P. Heinz at Wed Feb 08 19:34:05 EST 2017

LINKS

Wikipedia, <a href="httphttps://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

STATUS

approved

editing

#7 by Alois P. Heinz at Thu Oct 30 22:11:03 EDT 2014

STATUS

editing

approved

#6 by Alois P. Heinz at Thu Oct 30 22:10:47 EDT 2014

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)

a:= n-> `if`(n=0, 1, g (n, n, [])):

seq (a(n), n=0..20);

STATUS

approved

editing

#5 by Alois P. Heinz at Sun Oct 28 17:58:56 EDT 2012

STATUS

editing

approved

#4 by Alois P. Heinz at Sun Oct 28 17:57:52 EDT 2012

LINKS

Wikipedia, <a href="http://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

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:

g:= proc(n, i, l) `if`(n=0, h(l)^10, `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);

#3 by Alois P. Heinz at Sun Oct 28 17:56:47 EDT 2012

LINKS

Alois P. Heinz, <a href="/A218437/b218437.txt">Table of n, a(n) for n = 0..60</a>