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 A275327 Triangle read by rows, Riordan array (1, (2+(x-1)/(2*x^2)*(1-sqrt(1-4*x^2)))/ sqrt(1-4*x^2)). 2
 1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 2, 7, 3, 1, 0, 10, 10, 12, 4, 1, 0, 5, 33, 25, 18, 5, 1, 0, 35, 42, 78, 48, 25, 6, 1, 0, 14, 144, 144, 155, 80, 33, 7, 1, 0, 126, 168, 420, 356, 275, 122, 42, 8, 1, 0, 42, 610, 723, 1018, 736, 450, 175, 52, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS EXAMPLE Table starts: [n] [k=0,1,2,...] row sum [0] [1] 1 [1] [0, 1] 1 [2] [0, 1, 1] 2 [3] [0, 3, 2, 1] 6 [4] [0, 2, 7, 3, 1] 13 [5] [0, 10, 10, 12, 4, 1] 37 [6] [0, 5, 33, 25, 18, 5, 1] 87 [7] [0, 35, 42, 78, 48, 25, 6, 1] 235 [8] [0, 14, 144, 144, 155, 80, 33, 7, 1] 578 [9] [0, 126, 168, 420, 356, 275, 122, 42, 8, 1] 1518 MAPLE S := proc(n, k) option remember; local ecn: if n = 0 then return n^k fi; ecn := n -> n!/(iquo(n, 2)!^2)/(iquo(n, 2)+1); add(ecn(i)*S(n-1, k-i), i=1..k-n+1) end: A275327 := (n, k) -> S(k, n): seq(seq(A275327(n, k), k=0..n), n=0..8); MATHEMATICA (* The function RiordanArray is defined in A256893. *) RiordanArray[1&, (2+(#-1)/(2#^2) (1-Sqrt[1-4#^2]))/Sqrt[1-4#^2]&, 11] // Flatten (* Jean-François Alcover, Jul 16 2019 *) PROG (Sage) # Function riordan_array defined in A256893. s = (2+(x-1)/(2*x^2)*(1-sqrt(1-4*x^2)))/sqrt(1-4*x^2) riordan_array(1, s, 12) CROSSREFS Cf. A057977 (column 1), A128899, A275328. Sequence in context: A250486 A316826 A256449 * A215486 A083721 A158459 Adjacent sequences:  A275324 A275325 A275326 * A275328 A275329 A275330 KEYWORD nonn,tabl,changed AUTHOR Peter Luschny, Aug 16 2016 STATUS approved

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Last modified July 22 17:02 EDT 2019. Contains 325225 sequences. (Running on oeis4.)