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A109446
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Binomial coefficients C(n,k) with n-k even, read by rows.
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2
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1, 1, 1, 1, 3, 1, 1, 6, 1, 5, 10, 1, 1, 15, 15, 1, 7, 35, 21, 1, 1, 28, 70, 28, 1, 9, 84, 126, 36, 1, 1, 45, 210, 210, 45, 1, 11, 165, 462, 330, 55, 1, 1, 66, 495, 924, 495, 66, 1, 13, 286, 1287, 1716, 715, 78, 1, 1, 91, 1001, 3003, 3003, 1001, 91, 1, 15, 455, 3003, 6435, 5005
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OFFSET
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0,5
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COMMENTS
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Binomial(n,2(n-k-1)) is also the number of permutations avoiding both 123 and 132 with k descents, i.e., positions with w[i]>w[i+1]. - Lara Pudwell, Dec 19 2018
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LINKS
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EXAMPLE
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Starred terms in Pascal's triangle (A007318), read by rows:
1*;
1, 1*;
1*, 2, 1*;
1, 3*, 3, 1*;
1*, 4, 6*, 4, 1*;
1, 5*, 10, 10*, 5, 1*;
1*, 6, 15*, 20, 15*, 6, 1*;
1, 7*, 21, 35*, 35, 21*, 7, 1*;
1*, 8, 28*, 56, 70*, 56, 28*, 8, 1*;
1, 9*, 36, 84*, 126, 126*, 84, 36*, 9, 1*;
Rows in A086645 (1; 1, 1; 1, 6, 1; ...) interspersed with rows in A103327 (1; 3, 1; 5, 10, 1; ...).
1; 1; 1, 1; 3, 1; 1, 6, 1; 5, 10, 1; 1, 15, 15, 1; 7, 35, 21, 1; ....
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MAPLE
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T:= (n, k)-> binomial(n, 2*k+irem(n, 2)):
seq(seq(T(n, k), k=0..floor(n/2)), n=0..20); # Alois P. Heinz, Feb 07 2014
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MATHEMATICA
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Flatten[ Table[ If[ EvenQ[n - k], Binomial[n, k], {}], {n, 0, 15}, {k, 0, n}]] (* Robert G. Wilson v *)
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CROSSREFS
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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