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 A026009 Triangular array T read by rows: T(n,0) = 1 for n >= 0; T(1,1) = 1; and for n >= 2, T(n,k) = T(n-1,k-1) + T(n-1,k) for k = 1,2,...,[(n+1)/2]; T(n,n/2 + 1) = T(n-1,n/2) if n is even. 18

%I

%S 1,1,1,1,2,1,1,3,3,1,4,6,3,1,5,10,9,1,6,15,19,9,1,7,21,34,28,1,8,28,

%T 55,62,28,1,9,36,83,117,90,1,10,45,119,200,207,90,1,11,55,164,319,407,

%U 297,1,12,66,219,483,726,704,297,1,13,78,285,702,1209,1430,1001,1,14,91,363,987,1911

%N Triangular array T read by rows: T(n,0) = 1 for n >= 0; T(1,1) = 1; and for n >= 2, T(n,k) = T(n-1,k-1) + T(n-1,k) for k = 1,2,...,[(n+1)/2]; T(n,n/2 + 1) = T(n-1,n/2) if n is even.

%F T(n, k) = binomial(n, k) - binomial(n, k-3). - Darko Marinov (marinov(AT)lcs.mit.edu), May 17 2001

%e From _Jonathon Kirkpatrick_, Jul 01 2016: (Start)

%e Triangle begins:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 3, 3;

%e 1, 4, 6, 3;

%e 1, 5, 10, 9;

%e 1, 6, 15, 19, 9;

%e 1, 7, 21, 34, 28;

%e 1, 8, 28, 55, 62, 28;

%e 1, 9, 36, 83, 117, 90;

%e 1, 10, 45, 119, 200, 207, 90;

%e 1, 11, 55, 164, 319, 407, 297;

%e 1, 12, 66, 219, 483, 726, 704, 297;

%e 1, 13, 78, 285, 702, 1209, 1430, 1001;

%e ... (End)

%Y Cf. A026016, A000217.

%K nonn,tabf,easy

%O 1,5

%A _Clark Kimberling_

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)