A192250 - OEIS

%I #8 Dec 04 2016 19:46:25

%S 1,1,7,27,167,923,5543,32999,200309,1221329,7503033,46301793,

%T 286971677,1784658077,11131825877,69611130917,436270168817,

%U 2739539507957,17232530582057,108564692241257,684901029237677,4326215549824277,27357682806703397

%N 0-sequence of reduction of central binomial coefficient sequence by x^2 -> x+1.

%C See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]".

%F Conjecture: (n-1)*(n-2)*a(n) -(5*n-7)*(n-2)*a(n-1) -2*(2*n-3)*(3*n-8)*a(n-2) +4*(2*n-3)*(2*n-5)*a(n-3)=0. - _R. J. Mathar_, May 04 2014

%t c[n_] := (2 n)!/(n! n!); (* central binomial coefficients, A000984 *)

%t Table[c[n], {n, 0, 15}]

%t q[x_] := x + 1;

%t p[0, x_] := 1; p[n_, x_] := p[n - 1, x] + (x^n)*c[n]

%t reductionRules = {x^y_?EvenQ -> q[x]^(y/2),

%t    x^y_?OddQ -> x q[x]^((y - 1)/2)};

%t t = Table[Last[Most[FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,

%t    30}]

%t Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192250 *)

%t Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192251 *)

%t Table[Coefficient[Part[t, n]/2, x, 1], {n, 1, 30}]  (* A192070 *)

%t (* by _Peter J. C. Moses_, Jun 20 2011 *)

%Y Cf. A192232, A192251, A192070.

%K nonn

%O 1,3

%A _Clark Kimberling_, Jun 27 2011