A370051 Expansion of (1-5*x+6*x^2-x^3)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

1, 4, 14, 48, 165, 572, 2002, 7071, 25176, 90251, 325358, 1178291, 4282811, 15612092, 57040186, 208772476, 765186422, 2807556411, 10309833845, 37883902913, 139275229088, 512223805060, 1884404481767, 6934058102453, 25519786076294

Offset

0,2

Comments

In Pascal's triangle, subtract the 6th column to the left of the central column from the 2nd column.

Links

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1).

Formula

a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5); a(0) = 1, a(1) = 4, a(2) = 14, a(3) = 48, a(4) = 165.

Example

a(0) = binomial(2,0);
a(1) = binomial(4,1);
a(2) = binomial(6,2) - binomial(6,0);
a(3) = binomial(8,3) - binomial(8,1);
a(4) = binomial(10,4) - binomial(10,2).

Mathematica

LinearRecurrence[{9, -28, 35, -15, 1}, {1, 4, 14, 48, 165}, 30] (* Paolo Xausa, Feb 20 2024 *)

Crossrefs

Cf. A007318, A211216, A224422, A221863, A122588.

Sequence in context: A092489 A094827 A094667 * A099376 A002057 A047048

Adjacent sequences: A370048 A370049 A370050 * A370052 A370053 A370054

Keyword

nonn,easy

Author

Peter Morris, Feb 08 2024

Status

approved