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A049400 Partial sums of rows of A047884. Young Tableaux by height.

%I A049400 #28 Nov 21 2018 11:38:23
%S A049400 1,1,2,1,3,4,1,6,9,10,1,10,21,25,26,1,20,51,70,75,76,1,35,127,196,225,
%T A049400 231,232,1,70,323,588,715,756,763,764,1,126,835,1764,2347,2556,2611,
%U A049400 2619,2620,1,252,2188,5544,7990,9096,9415,9486,9495,9496,1,462,5798,17424,27908,33231,35135,35596
%N A049400 Partial sums of rows of A047884. Young Tableaux by height.
%H A049400 Seiichi Manyama, <a href="/A049400/b049400.txt">Rows n = 1..70, flattened</a> (first 44 rows from Alois P. Heinz)
%H A049400 <a href="/index/Y#Young">Index entries for sequences related to Young tableaux.</a>
%e A049400 1;
%e A049400 1,  2;
%e A049400 1,  3,   4;
%e A049400 1,  6,   9,  10;
%e A049400 1, 10,  21,  25,  26;
%e A049400 1, 20,  51,  70,  75,  76;
%e A049400 1, 35, 127, 196, 225, 231, 232;
%e A049400 1, 70, 323, 588, 715, 756, 763, 764;
%p A049400 h:= proc(l) local n; n:=nops(l); add(i, i=l)! /mul(mul(1+l[i]-j+
%p A049400       add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
%p A049400     end:
%p A049400 g:= proc(n, i, l) option remember;
%p A049400       `if`(n=0, h(l), `if`(i<1, 0, `if`(i=1, h([l[], 1$n]), g(n, i-1, l)+
%p A049400       `if`(i>n, 0, g(n-i, i, [l[], i])))))
%p A049400     end:
%p A049400 T:= (n, k)-> g(n, k, []):
%p A049400 seq(seq(T(n, k), k=1..n), n=1..12); # _Alois P. Heinz_, Apr 16 2012
%t A049400 Accumulate /@ Table[ Plus @@ NumberOfTableaux /@ Reverse /@ Union[ Sort /@ (Compositions[n - m, m] + 1)], {n, 1, 12}, {m, 1, n}] // Flatten (* _Jean-François Alcover_, Jan 29 2013, after Mathematica program for A047884 *)
%Y A049400 Cf. A000085, A007579, A007578, A007580, A049401, A293128.
%K A049400 easy,nice,nonn,tabl
%O A049400 1,3
%A A049400 _Alford Arnold_