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 A210863 Triangle of coefficients of polynomials v(n,x) jointly generated with A210862; see the Formula section. 3
 1, 1, 2, 4, 5, 3, 9, 13, 13, 5, 16, 37, 47, 32, 8, 25, 96, 152, 147, 73, 13, 36, 217, 469, 587, 432, 158, 21, 49, 435, 1344, 2127, 2090, 1183, 330, 34, 64, 793, 3487, 7186, 8979, 6965, 3064, 669, 55, 81, 1342, 8179, 22544, 35296, 35304, 21754, 7577 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For n>1, row n starts with (n-1)^2 and ends with F(n+1), where F=A000045 (Fibonacci numbers). For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=u(n-1,x)+x*v(n-1,x)+1, v(n,x)=(x+n-1)*u(n-1,x)+x*v(n-1,x), where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 1....2 4....5....3 9....13...13...5 16...37...47...32...8 First three polynomials v(n,x): 1, 1 + 2x, 4 + 5x + 3x^2 MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 14; u[n_, x_] := u[n - 1, x] + x*v[n - 1, x] + 1; v[n_, x_] := (x + n - 1)*u[n - 1, x] + x*v[n - 1, x]; 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[%]   (* A210862 *) cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]   (* A210863 *) CROSSREFS Cf. A210862, A208510. Sequence in context: A097292 A269780 A038776 * A245816 A118461 A266408 Adjacent sequences:  A210860 A210861 A210862 * A210864 A210865 A210866 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 28 2012 STATUS approved

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Last modified October 16 16:13 EDT 2019. Contains 328101 sequences. (Running on oeis4.)