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 A114123 Riordan array (1/(1-x), x(1+x)^2/(1-x)^2). 5
 1, 1, 1, 1, 5, 1, 1, 13, 9, 1, 1, 25, 41, 13, 1, 1, 41, 129, 85, 17, 1, 1, 61, 321, 377, 145, 21, 1, 1, 85, 681, 1289, 833, 221, 25, 1, 1, 113, 1289, 3653, 3649, 1561, 313, 29, 1, 1, 145, 2241, 8989, 13073, 8361, 2625, 421, 33, 1, 1, 181, 3649, 19825, 40081, 36365, 16641, 4089, 545, 37, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are A099463(n+1). Diagonal sums are A116404. Triangle formed of even-numbered columns of the Delannoy triangle A008288. - Philippe Deléham, Mar 11 2013 LINKS FORMULA T(n,k) = Sum_{j=0..n} C(2k,n-k-j)*C(n-k,j)*2^(n-k-j). T(n,k) = Sum_{j=0..n-k} C(2k,j)C(n-k,j)*2^j. T(n,k) = hypergeom([-2*k, k-n], [1], 2). - Peter Luschny, Sep 16 2014 EXAMPLE Triangle begins 1, 1, 1, 1, 5, 1, 1, 13, 9, 1, 1, 25, 41, 13, 1, 1, 41, 129, 85, 17, 1, 1, 61, 321, 377, 145, 21, 1 MAPLE T := (n, k) -> hypergeom([-2*k, k-n], [1], 2); seq(seq(round(evalf(T(n, k), 99)), k=0..n), n=0..9); # Peter Luschny, Sep 16 2014 MATHEMATICA T[n_, k_] := Hypergeometric2F1[-2k, k-n, 1, 2]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] (* Jean-François Alcover, Jun 13 2019 *) CROSSREFS Sequence in context: A299221 A300035 A130227 * A324009 A143007 A152654 Adjacent sequences:  A114120 A114121 A114122 * A114124 A114125 A114126 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Feb 07 2006, Oct 22 2006 STATUS approved

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Last modified May 26 08:31 EDT 2020. Contains 334620 sequences. (Running on oeis4.)