A360606 The polygonal polynomials evaluated at x = 1/2 and normalized with 2^n.

0, 1, 4, 13, 40, 117, 324, 853, 2152, 5245, 12436, 28845, 65736, 147685, 327940, 721189, 1573192, 3408237, 7340436, 15729085, 33554920, 71303701, 150995524, 318767733, 671089320, 1409286877, 2952790804, 6174016333, 12884902792, 26843546565, 55834575876

Offset

0,3

Comments

The coefficients of the polygonal polynomials are antidiagonals of A139600.

Links

Table of n, a(n) for n=0..30.

Formula

a(n) = 2^n * Sum_{k=0..n} A139600(n, k) * 2^(-k).

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

a(n) = 8 + 4*n + n^2 + (n-4) * 2^(n+1). - Vaclav Kotesovec, Feb 21 2023

Maple

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

Crossrefs

Cf. A139600, A360605.

Sequence in context: A272581 A342159 A191132 * A119915 A307577 A137744

Adjacent sequences: A360603 A360604 A360605 * A360607 A360608 A360609

Keyword

nonn

Author

Peter Luschny, Feb 13 2023

Status

approved