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A112973
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Riordan array (1/(1-x-x^2), x(1+x)/(1-x-x^2)^2).
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0
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1, 1, 1, 2, 4, 1, 3, 12, 7, 1, 5, 31, 31, 10, 1, 8, 73, 110, 59, 13, 1, 13, 162, 340, 267, 96, 16, 1, 21, 344, 956, 1022, 529, 142, 19, 1, 34, 707, 2507, 3479, 2416, 923, 197, 22, 1, 55, 1416, 6231, 10850, 9657, 4900, 1476, 261, 25, 1, 89, 2778, 14840, 31606, 34905
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) - 2*T(n-3,k) - T(n-4,k), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 4, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Jan 21 2014
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EXAMPLE
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Rows begin
1;
1,1;
2,4,1;
3,12,7,1;
5,31,31,10,1;
8,73,110,59,13,1;
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PROG
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(Maxima) T(n, k):=sum(binomial(m, n-m)*binomial(m+k, 2*k), m, floor(n/2), n); /* Vladimir Kruchinin, Apr 21 2015 */
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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