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A275328 Triangle read by rows, Riordan array (1, (1+x/(1-4*x^2))/sqrt(1-4*x^2). 2

%I

%S 1,0,1,0,2,1,0,6,4,1,0,6,16,6,1,0,30,36,30,8,1,0,20,120,98,48,10,1,0,

%T 140,232,342,200,70,12,1,0,70,756,924,784,350,96,14,1,0,630,1300,2856,

%U 2576,1550,556,126,16,1

%N Triangle read by rows, Riordan array (1, (1+x/(1-4*x^2))/sqrt(1-4*x^2).

%e Table starts:

%e [n] [k=0,1,2,...] row sum

%e [0], [1], 1

%e [1], [0, 1], 1

%e [2], [0, 2, 1], 3

%e [3], [0, 6, 4, 1], 11

%e [4], [0, 6, 16, 6, 1], 29

%e [5], [0, 30, 36, 30, 8, 1], 105

%e [6], [0, 20, 120, 98, 48, 10, 1], 297

%e [7], [0, 140, 232, 342, 200, 70, 12, 1], 997

%e [8], [0, 70, 756, 924, 784, 350, 96, 14, 1], 2995

%e [9], [0, 630, 1300, 2856, 2576, 1550, 556, 126, 16, 1], 9611

%p S := proc(n, k) option remember; local sf: if n = 0 then return n^k fi;

%p sf := n -> n!/iquo(n, 2)!^2; add(sf(i)*S(n-1, k-i), i=1..k-n+1) end:

%p A275328 := (n, k) -> S(k, n): seq(seq(A275328(n, k), k=0..n), n=0..8);

%t (* The function RiordanArray is defined in A256893. *)

%t RiordanArray[1&, (1+#/(1-4#^2))/Sqrt[1-4#^2]&, 10] // Flatten (* _Jean-Fran├žois Alcover_, Jul 16 2019 *)

%o (Sage) # uses[riordan_array from A256893]

%o riordan_array(1, (1+x/(1-4*x^2))/sqrt(1-4*x^2), 10)

%Y Cf. A056040 (column 1), A275327.

%K nonn,tabl

%O 0,5

%A _Peter Luschny_, Aug 19 2016

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Last modified May 26 00:08 EDT 2020. Contains 334613 sequences. (Running on oeis4.)