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 A112519 Riordan array (1,xc(x)*c(-xc(x))), c(x) the g.f. of A000108. 3
 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 4, 0, 1, 0, 12, 2, 6, 0, 1, 0, 14, 28, 3, 8, 0, 1, 0, 100, 32, 48, 4, 10, 0, 1, 0, 180, 249, 54, 72, 5, 12, 0, 1, 0, 990, 440, 455, 80, 100, 6, 14, 0, 1, 0, 2310, 2552, 792, 726, 110, 132, 7, 16, 0, 1, 0, 10920, 5876, 4836, 1248, 1070, 144, 168, 8, 18, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Row sums are A112520. Second column is essentially A055392. Inverse is A112517. Riordan array product (1,xc(x))*(1,xc(-x)). LINKS FORMULA Riordan array (1, (sqrt(3-2*sqrt(1-4x))-1)/2); Number triangle T(0, 0)=1, T(n, k)=sum{j=0..n, (k/n)(-1)^(j-k)C(2n-j-1, n-j)C(2j-k-1, j-k)}. EXAMPLE Triangle begins .1; .0,1; .0,0,1; .0,2,0,1; .0,1,4,0,1; .0,12,2,6,0,1; MATHEMATICA c[x_] := (1 - Sqrt[1 - 4 x])/(2 x); (* The function RiordanArray is defined in A256893. *) RiordanArray[1&, # c[#] c[-# c[#]]&, 12] // Flatten (* Jean-François Alcover, Jul 16 2019 *) CROSSREFS Sequence in context: A185370 A066745 A112517 * A276981 A230305 A091728 Adjacent sequences:  A112516 A112517 A112518 * A112520 A112521 A112522 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Sep 09 2005 STATUS approved

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Last modified June 22 21:25 EDT 2021. Contains 345392 sequences. (Running on oeis4.)