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

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, 140, 232, 342, 200, 70, 12, 1, 0, 70, 756, 924, 784, 350, 96, 14, 1, 0, 630, 1300, 2856, 2576, 1550, 556, 126, 16, 1

Offset: 0

Author

Peter Luschny, Aug 19 2016

Keywords

• nonn
• tabl

Examples

			Table starts:
[n] [k=0,1,2,...] row sum
[0], [1], 1
[1], [0, 1], 1
[2], [0, 2, 1], 3
[3], [0, 6, 4, 1], 11
[4], [0, 6, 16, 6, 1], 29
[5], [0, 30, 36, 30, 8, 1], 105
[6], [0, 20, 120, 98, 48, 10, 1], 297
[7], [0, 140, 232, 342, 200, 70, 12, 1], 997
[8], [0, 70, 756, 924, 784, 350, 96, 14, 1], 2995
[9], [0, 630, 1300, 2856, 2576, 1550, 556, 126, 16, 1], 9611
		

Crossrefs

Cf. A056040 (column 1), A275327.

Programs

Maple

S := proc(n, k) option remember; local sf: if n = 0 then return n^k fi;
sf := n -> n!/iquo(n, 2)!^2; add(sf(i)*S(n-1, k-i), i=1..k-n+1) end:
A275328 := (n, k) -> S(k, n): seq(seq(A275328(n, k), k=0..n), n=0..8);

Mathematica

(* The function RiordanArray is defined in A256893. *)
RiordanArray[1&, (1+#/(1-4#^2))/Sqrt[1-4#^2]&, 10] // Flatten (* Jean-François Alcover, Jul 16 2019 *)

SageMath

# uses[riordan_array from A256893]
riordan_array(1, (1+x/(1-4*x^2))/sqrt(1-4*x^2), 10)