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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

Table of n, a(n) for n=0..65.

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.)