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 A236934 Triangle of Poupard numbers g_n(k) read by rows, n>=1, 1<=k<=2n-1. 2
 1, 0, 2, 0, 0, 4, 8, 4, 0, 0, 32, 64, 80, 64, 32, 0, 0, 544, 1088, 1504, 1664, 1504, 1088, 544, 0, 0, 15872, 31744, 45440, 54784, 58112, 54784, 45440, 31744, 15872, 0, 0, 707584, 1415168, 2059264, 2576384, 2911744, 3027968, 2911744, 2576384, 2059264, 1415168, 707584, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Peter Luschny, Row(n) for n = 1..25 Dominique Foata and Guo-Niu Han, Seidel Triangle Sequences and Bi-Entringer Numbers, November 20, 2013. Christiane Poupard, Deux propriétés des arbres binaires ordonnés stricts, Europ. J. Combin., vol. 10, 1989, p. 369-374. FORMULA 4^(-n)*sum(k=1..2*n+1, binomial(2*n,k-1)*T(n+1,k)) = A000364(n), n>=0. - Peter Luschny, May 11 2014 (-1)^n*sum(k=1..2*n+1, (-1)^(k-1)*binomial(2*n,k-1)*T(n+1,k)) = A000302(n), n>=0. - Peter Luschny, May 11 2014 EXAMPLE Triangle begins: 1, 0, 2, 0, 0, 4, 8, 4, 0, 0, 32, 64, 80, 64, 32, 0, 0, 544, 1088, 1504, 1664, 1504, 1088, 544, 0, ... MAPLE T := proc(n, k) option remember; local j;   if n = 1 then 1 elif k = 1 then 0 elif k = 2 then 2*add(T(n-1, j), j=1..2*n-3) elif k > n then T(n, 2*n-k) else 2*T(n, k-1)-T(n, k-2)-4*T(n-1, k-2)   fi end: seq(print(seq(T(n, k), k=1..2*n-1)), n=1..6); # Peter Luschny, May 11 2014 MATHEMATICA T[n_, k_] /; 1 <= k <= 2n-1 := T[n, k] = Which[n == 1, 1, k == 1, 0, k == 2, 2 Sum[T[n-1, j], {j, 1, 2n-3}], k > n, T[n, 2n-k], True, 2 T[n, k-1] - T[n, k-2] - 4 T[n-1, k-2]]; T[_, _] = 0; Table[T[n, k], {n, 1, 7}, {k, 1, 2n-1}] // Flatten (* Jean-François Alcover, Jul 08 2019, from Maple *) CROSSREFS Cf. A000182 (row sums), A008282, A125053. Sequence in context: A056676 A098699 A021837 * A155719 A153772 A197007 Adjacent sequences:  A236931 A236932 A236933 * A236935 A236936 A236937 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Feb 17 2014 EXTENSIONS More terms from Peter Luschny, May 11 2014 STATUS approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)