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Search: id:A126445
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| A126445 |
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Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3), n-k) for n>=k>=0. |
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10
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| 1, 1, 1, 6, 3, 1, 120, 36, 6, 1, 4845, 969, 120, 10, 1, 324632, 46376, 4495, 300, 15, 1, 32468436, 3478761, 270725, 15180, 630, 21, 1, 4529365776, 377447148, 24040016, 1150626, 41664, 1176, 28, 1, 840261910995, 56017460733, 2967205528, 122391522
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Amazingly, A126460 = A126445^-1*A126450 = A126450^-1*A126454 = A126454^-1*A126457; and also A126465 = A126450*A126445^-1 = A126454*A126450^-1 = A126457*A126454^-1.
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FORMULA
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T(n,k) = C( n*(n+1)*(n+2)/3! - k*(k+1)*(k+2)/3!, n-k) for n>=k>=0.
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EXAMPLE
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Formula: T(n,k) = C( C(n+2,3) - C(k+2,3), n-k) is illustrated by:
T(n=4,k=1) = C( C(6,3) - C(3,3), n-k) = C(19,3) = 969;
T(n=4,k=2) = C( C(6,3) - C(4,3), n-k) = C(16,2) = 120;
T(n=5,k=2) = C( C(7,3) - C(4,3), n-k) = C(31,3) = 4495.
Triangle begins:
1;
1, 1;
6, 3, 1;
120, 36, 6, 1;
4845, 969, 120, 10, 1;
324632, 46376, 4495, 300, 15, 1;
32468436, 3478761, 270725, 15180, 630, 21, 1;
4529365776, 377447148, 24040016, 1150626, 41664, 1176, 28, 1; ...
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PROGRAM
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(PARI) T(n, k)=binomial(n*(n+1)*(n+2)/3!-k*(k+1)*(k+2)/3!, n-k)
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CROSSREFS
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Columns: A126446, A126447, A126448; A126449 (row sums); variants: A126450, A126454, A126457, A107862.
Sequence in context: A119743 A108451 A122178 this_sequence A033326 A068996 A068924
Adjacent sequences: A126442 A126443 A126444 this_sequence A126446 A126447 A126448
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 27 2006
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