Young tableaux cont

John Conway conway at math.Princeton.EDU
Wed May 12 16:10:03 CEST 1999

On Wed, 12 May 1999, N. J. A. Sloane wrote:

> yes, i'm very interested, and i added this entry to the database
> %I A047884
> %S A047884 1,1,1,1,2,1,1,5,3,1,1,9,11,4,1,1,19,31,19,5,1,1,34,92,69,29,6,1,1,
> %T A047884 69,253,265,127,41,7,1,1,125,709,929,583,209,55,8,1,1,251,1936,3356,
> %U A047884 2446,1106,319,71,9,1,1,461,5336,11626,10484,5323,1904,461,89,10,1
> %N A047884 Triangle of numbers a(n,k) = no. of Young tableaux corresponding to partiti
> ons of n into exactly k parts.

   This is an unnecessarily long title (or, if I'm misunderstanding it,
a misleading one) - it would be better to delete the words
"Young tableaux corresponding to".

    A similar comment applies to the next one:
> %I A000085 M1221 N0469
> %S A000085 1,1,2,4,10,26,76,232,764,2620,9496,35696,140152,568504,2390480,
> %T A000085 10349536,46206736,211799312,997313824,4809701440,23758664096,
> %U A000085 119952692896,618884638912,3257843882624,17492190577600,95680443760576
> %N A000085 Self-inverse permutations on n letters; Young tableaux with n cells.
> %F A000085 a(n) = a(n-1) + (n-1)*a(n-2).

     John Conway

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