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Search: id:A102539
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| A102539 |
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Square array T(n,k) read by antidiagonals: Prod[1<=i<=j<=k, (n+i+j-1)/(i+j-1) ]. |
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6
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| 2, 3, 4, 4, 10, 8, 5, 20, 35, 16, 6, 35, 112, 126, 32, 7, 56, 294, 672, 462, 64, 8, 84, 672, 2772, 4224, 1716, 128, 9, 120, 1386, 9504, 28314, 27456, 6435, 256, 10, 165, 2640, 28314, 151008, 306735, 183040, 24310, 512, 11, 220, 4719, 75504, 674817
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Number of semistandard Young tableaux with at most n columns and with entries in [k].
T(n,k) is the number of k X k symmetric matrices with entries in 0..n with each row (and column) in nondecreasing order. - Ron Hardin (rhhardin(AT)att.net), Jul 08 2008
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LINKS
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M. Lederer, A determinant-like formula for the Kostka numbers
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FORMULA
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It appears that T is identical to the reflected triangle A073165, i.e. T(n, k) = Prod[i=1..floor((k+1)/2), C(n+k+2i-1-(k mod 2), 4i-1-2(k mod 2))] / Prod[i=0..floor((k-1)/2), C(2k-2i-1, 2i)].
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EXAMPLE
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2,4,8,16,32,64
3,10,35,126,462,1716
4,20,112,672,4224,27456
5,35,294,2772,28314,306735
6,56,672,9504,151008,2617472
7,84,1386,28314,674817,18076916
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CROSSREFS
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Rows include A000079, A001700, A003645, A000356. Main diagonal is A049505.
Sequence in context: A097093 A056877 A118263 this_sequence A118022 A037848 A037884
Adjacent sequences: A102536 A102537 A102538 this_sequence A102540 A102541 A102542
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 14 2005
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