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

%I A275328 #16 Dec 13 2023 00:34:09
%S A275328 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 A275328 140,232,342,200,70,12,1,0,70,756,924,784,350,96,14,1,0,630,1300,2856,
%U A275328 2576,1550,556,126,16,1
%N A275328 Triangle read by rows, Riordan array [1, (1+x/(1-4*x^2))/sqrt(1-4*x^2)].
%e A275328 Table starts:
%e A275328 [n] [k=0,1,2,...] row sum
%e A275328 [0], [1], 1
%e A275328 [1], [0, 1], 1
%e A275328 [2], [0, 2, 1], 3
%e A275328 [3], [0, 6, 4, 1], 11
%e A275328 [4], [0, 6, 16, 6, 1], 29
%e A275328 [5], [0, 30, 36, 30, 8, 1], 105
%e A275328 [6], [0, 20, 120, 98, 48, 10, 1], 297
%e A275328 [7], [0, 140, 232, 342, 200, 70, 12, 1], 997
%e A275328 [8], [0, 70, 756, 924, 784, 350, 96, 14, 1], 2995
%e A275328 [9], [0, 630, 1300, 2856, 2576, 1550, 556, 126, 16, 1], 9611
%p A275328 S := proc(n, k) option remember; local sf: if n = 0 then return n^k fi;
%p A275328 sf := n -> n!/iquo(n, 2)!^2; add(sf(i)*S(n-1, k-i), i=1..k-n+1) end:
%p A275328 A275328 := (n, k) -> S(k, n): seq(seq(A275328(n, k), k=0..n), n=0..8);
%t A275328 (* The function RiordanArray is defined in A256893. *)
%t A275328 RiordanArray[1&, (1+#/(1-4#^2))/Sqrt[1-4#^2]&, 10] // Flatten (* _Jean-François Alcover_, Jul 16 2019 *)
%o A275328 (SageMath) # uses[riordan_array from A256893]
%o A275328 riordan_array(1, (1+x/(1-4*x^2))/sqrt(1-4*x^2), 10)
%Y A275328 Cf. A056040 (column 1), A275327.
%K A275328 nonn,tabl
%O A275328 0,5
%A A275328 _Peter Luschny_, Aug 19 2016