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%I #5 Feb 02 2020 16:55:09
%S 1,3,21,171,1509,13995,134277,1320651,13237221,134682219,1387100229,
%T 14430764043,151415596197,1600364733867,17022016484613,
%U 182055719885643,1956671540189541,21121180251536619,228880429935661509,2488986535173458571,27152943714786745893
%N Evaluation of the Little-Schröder polynomials at 1/2 and normalized with 2^n.
%F a(n) = 2^n*Sum_{k=0..n} A172094(n,k) / 2^k.
%F a(n) = [x^n] (1 + 6*x - 3*(4*x^2 - 12*x + 1)^(1/2))/(30*x - 2).
%F a(n) = (60*(n - 3)*a(n-3) + (282 - 184*n)*a(n-2) + (27*n - 18)*a(n-1)) / n.
%p gf := (1+6*x-3*(4*x^2-12*x+1)^(1/2))/(30*x-2): ser := series(gf, x, 32):
%p seq(coeff(ser, x, n), n=0..20);
%t RecurrenceTable[{a[n] == (60 a[n - 3] (n - 3) + (-184 n + 282) a[n - 2] + (27*n - 18) a[n - 1])/n, a[0] == 1, a[1] == 3, a[2] == 21}, a, {n, 20}]
%Y Cf. A172094, A001003, A330802.
%K nonn
%O 0,2
%A _Peter Luschny_, Feb 02 2020