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A101603 Riordan array (1/(1-x^2), x(1+x)/(1-x)). 3
1, 0, 1, 1, 2, 1, 0, 3, 4, 1, 1, 4, 9, 6, 1, 0, 5, 16, 19, 8, 1, 1, 6, 25, 44, 33, 10, 1, 0, 7, 36, 85, 96, 51, 12, 1, 1, 8, 49, 146, 225, 180, 73, 14, 1, 0, 9, 64, 231, 456, 501, 304, 99, 16, 1, 1, 10, 81, 344, 833, 1182, 985, 476, 129, 18, 1, 0, 11, 100, 489, 1408, 2471, 2668 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
Columns are generated by x^k*(1+x)^(k-1)/(1-x)^(k+1).
T(n, k) = Sum_{j=0..n-k} C(k-1, j)*C(n-j, n-k-j).
T(n, k) = (n - k + 1)*hypergeom([1 - k, k - n], [2], 2). - Peter Luschny, Mar 09 2022
EXAMPLE
Rows start
1;
0, 1;
1, 2, 1;
0, 3, 4, 1;
1, 4, 9, 6, 1;
0, 5, 16, 19, 8, 1;
MATHEMATICA
t[n_, k_] := Binomial[n+k, k]*Hypergeometric2F1[-k+1, -n, -n-k, -1]; Table[t[n-k, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 22 2013 *)
CROSSREFS
Cf. A119328 (row-reversed).
Row sums are A097076(n+1).
Diagonal sums are abs(A077902).
Sequence in context: A345117 A188286 A363154 * A228161 A124030 A166040
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Dec 08 2004
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)