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 A210220 T(n, k) = -binomial(2*n-k+2, k+1)*hypergeom([2*n-k+3, 1], [k+2], 2). Triangle read by rows, T(n, k) for 1 <= k <= n. 4
 1, 2, 2, 3, 6, 3, 4, 12, 13, 4, 5, 20, 34, 24, 5, 6, 30, 70, 80, 40, 6, 7, 42, 125, 200, 166, 62, 7, 8, 56, 203, 420, 496, 314, 91, 8, 9, 72, 308, 784, 1211, 1106, 553, 128, 9, 10, 90, 444, 1344, 2576, 3108, 2269, 920, 174, 10, 11, 110, 615, 2160, 4956, 7476, 7274, 4352, 1461, 230, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Previous name: Triangle of coefficients of polynomials v(n,x) jointly generated with A210217. For a discussion and guide to related arrays, see A208510. LINKS Table of n, a(n) for n=1..66. FORMULA First and last term in row n: n. Column 2: n*(n-1). Column 3: A016061. Column 4: A112742. Row sums: -1+(even-indexed Fibonacci numbers). Periodic alternating row sums: 1,0,0,1,0,0,1,0,0,... u(n,x)=x*u(n-1,x)+v(n-1,x)+1, v(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 2...2 3...6....3 4...12...13...4 5...20...34...24...5 First three polynomials v(n,x): 1, 2 + 2x , 3 + 6x + 3x^2. MAPLE T := (n, k) -> -binomial(2*n-k+2, k+1)*hypergeom([2*n-k+3, 1], [k+2], 2): seq(seq(simplify(T(n, k)), k=1..n), n=1..10); # Peter Luschny, Oct 31 2019 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1; v[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%] (* A210219 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A210220 *) CROSSREFS Cf. A210219, A208510, A016061, A112742. Sequence in context: A329655 A183474 A294034 * A075196 A196912 A197079 Adjacent sequences: A210217 A210218 A210219 * A210221 A210222 A210223 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 19 2012 EXTENSIONS New name from Peter Luschny, Oct 31 2019 STATUS approved

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Last modified October 4 19:37 EDT 2023. Contains 365888 sequences. (Running on oeis4.)