A395505 - OEIS

A395505

Triangle of polynomials refining A367255.

1, 1, 1, 1, 4, 2, 1, 9, 21, 9, 1, 16, 84, 160, 64, 1, 25, 230, 950, 1625, 625, 1, 36, 510, 3600, 12960, 20736, 7776, 1, 49, 987, 10535, 63455, 208887, 319333, 117649, 1, 64, 1736, 25984, 232960, 1261568, 3899392, 5767168, 2097152

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OFFSET

0,5

COMMENTS

The cases when n=0,1 are a bit special, involving some cancellations.

LINKS

Table of n, a(n) for n=0..44.

FORMULA

The n-th row is given by the polynomial (1+x*n)^(n-2)*(1+2*n*x+n*x^2).

EXAMPLE

The first few rows are:

1, 1;

1, 4, 2;

1, 9, 21, 9;

1, 16, 84, 160, 64;

1, 25, 230, 950, 1625, 625;

...

MATHEMATICA

row[n_]:=CoefficientList[(1+x*n)^(n-2)*(1+2*n*x+n*x^2), x]; Array[row, 9, 0]//Flatten (* Stefano Spezia, Apr 26 2026 *)

PROG

(SageMath)

x = polygen(QQ, 'x')

def row(n):

return (1+x*n)**(n-2)*(1+2*n*x+n*x**2)

(PARI) row(n) = Vecrev((1+x*n)^(n-2)*(1+2*n*x+n*x^2)); \\ Michel Marcus, Apr 26 2026

CROSSREFS

Cf. A000169, A367255.

Sequence in context: A021010 A342088 A193607 * A358735 A075397 A049429

Adjacent sequences: A395502 A395503 A395504 * A395506 A395507 A395508

KEYWORD

nonn,tabl

AUTHOR

F. Chapoton, Apr 26 2026

STATUS

approved