A331328 Evaluation of the Little-Schröder polynomials at 1/2 and normalized with 2^n.

1, 3, 21, 171, 1509, 13995, 134277, 1320651, 13237221, 134682219, 1387100229, 14430764043, 151415596197, 1600364733867, 17022016484613, 182055719885643, 1956671540189541, 21121180251536619, 228880429935661509, 2488986535173458571, 27152943714786745893

Offset: 0

Author

Peter Luschny, Feb 02 2020

Keywords

• nonn

Crossrefs

Cf. A172094, A001003, A330802.

Programs

Maple

gf := (1+6*x-3*(4*x^2-12*x+1)^(1/2))/(30*x-2): ser := series(gf, x, 32):
seq(coeff(ser, x, n), n=0..20);

Mathematica

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}]

Formula

a(n) = 2^n*Sum_{k=0..n} A172094(n,k) / 2^k.

a(n) = [x^n] (1 + 6*x - 3*(4*x^2 - 12*x + 1)^(1/2))/(30*x - 2).

a(n) = (60*(n - 3)*a(n-3) + (282 - 184*n)*a(n-2) + (27*n - 18)*a(n-1)) / n.