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 A229053 Number of standard Young tableaux of n cells and height <= 11. 3
 1, 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, 35696, 140151, 568491, 2390311, 10347911, 46191551, 211671999, 996269310, 4801547628, 23695885170, 119481280210, 615372604033, 3232009497979, 17302866542177, 94301143232321, 522945331559246, 2947729723188352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec and Alois P. Heinz, Table of n, a(n) for n = 0..400 FORMULA 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). a(n) ~ 40186125/1024 * 11^(n+55/2)/(Pi^(5/2)*n^(55/2)). Conjecture: a(n) ~ k^n/Pi^(k/2)*(k/n)^(k*(k-1)/4) * prod(j=1,k,Gamma(j/2)). MATHEMATICA 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}] CROSSREFS 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). Column k=11 of A182172. Cf. A000085. Sequence in context: A239081 A212916 A239082 * A229068 A000085 A222319 Adjacent sequences:  A229050 A229051 A229052 * A229054 A229055 A229056 KEYWORD nonn AUTHOR Vaclav Kotesovec, Sep 12 2013 STATUS approved

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Last modified January 19 09:35 EST 2019. Contains 319306 sequences. (Running on oeis4.)