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%I #18 Sep 16 2013 18:07:44
%S 1,1,2,4,10,26,76,232,764,2620,9496,35696,140151,568491,2390311,
%T 10347911,46191551,211671999,996269310,4801547628,23695885170,
%U 119481280210,615372604033,3232009497979,17302866542177,94301143232321,522945331559246,2947729723188352
%N Number of standard Young tableaux of n cells and height <= 11.
%H Vaclav Kotesovec and Alois P. Heinz, <a href="/A229053/b229053.txt">Table of n, a(n) for n = 0..400</a>
%H <a href="/index/Y#Young">Index entries for sequences related to Young tableaux.</a>
%F Recurrence: (n+10)*(n+18)*(n+24)*(n+28)*(n+30)*a(n) = (6*n^5 + 535*n^4 + 17752*n^3 + 265085*n^2 + 1658520*n + 2755377)*a(n-1) + (n-1)*(125*n^4 + 7472*n^3 + 149299*n^2 + 1090536*n + 1857231)*a(n-2) - 2*(n-2)*(n-1)*(270*n^3 + 11843*n^2 + 154023*n + 546120)*a(n-3) - (n-3)*(n-2)*(n-1)*(3319*n^2 + 74458*n + 331317)*a(n-4) + 3*(n-4)*(n-3)*(n-2)*(n-1)*(2578*n + 28701)*a(n-5) + 10395*(n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-6).
%F a(n) ~ 40186125/1024 * 11^(n+55/2)/(Pi^(5/2)*n^(55/2)).
%F Conjecture: a(n) ~ k^n/Pi^(k/2)*(k/n)^(k*(k-1)/4) * prod(j=1,k,Gamma(j/2)).
%t RecurrenceTable[{-10395 (-5+n) (-4+n) (-3+n) (-2+n) (-1+n) a[-6+n]-3 (-4+n) (-3+n) (-2+n) (-1+n) (28701+2578 n) a[-5+n]+(-3+n) (-2+n) (-1+n) (331317+74458 n+3319 n^2) a[-4+n]+2 (-2+n) (-1+n) (546120+154023 n+11843 n^2+270 n^3) a[-3+n]-(-1+n) (1857231+1090536 n+149299 n^2+7472 n^3+125 n^4) a[-2+n]+(-2755377-1658520 n-265085 n^2-17752 n^3-535 n^4-6 n^5) a[-1+n]+(10+n) (18+n) (24+n) (28+n) (30+n) a[n]==0,a[1]==1,a[2]==2,a[3]==4,a[4]==10,a[5]==26,a[6]==76}, a, {n, 20}]
%Y Cf. A182172, A001405 (k=2), A001006 (k=3), A005817 (k=4), A049401 (k=5), A007579 (k=6), A007578 (k=7), A007580 (k=8), A212915 (k=9), A212916 (k=10).
%Y Column k=11 of A182172.
%Y Cf. A000085.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Sep 12 2013
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