A385898 a(n) = 16*n^5 + 70*n^4 + 105*n^3 + 65*n^2 + 15*n + 1.

1, 272, 2763, 13024, 42125, 108576, 240247, 476288, 869049, 1486000, 2411651, 3749472, 5623813, 8181824, 11595375, 16062976, 21811697, 29099088, 38215099, 49484000, 63266301, 79960672, 100005863, 123882624, 152115625, 185275376, 223980147, 268897888, 320748149

Offset: 0

Author

Peter Luschny, Jul 21 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A385896 (column 6).

Programs

Maple

gf := (x^4 + 506*x^3 + 1146*x^2 + 266*x + 1)/(x - 1)^6:
ser := series(gf, x, 30): seq(coeff(ser, x, n), n = 0..28);

Mathematica

a[n_]:=16n^5+70n^4+105n^3+65n^2+15n+1;Array[a,29,0] (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{1, 272, 2763, 13024, 42125, 108576},29] (* or *) CoefficientList[Series[ (x^4 + 506*x^3 + 1146*x^2 + 266*x + 1)/(x - 1)^6,{x,0,28}],x] (* James C. McMahon, Jul 24 2025 *)

Formula

a(n) = [x^n] (x^4 + 506*x^3 + 1146*x^2 + 266*x + 1)/(x - 1)^6.

a(n) = 6! * [x^6] (1 - sin(n*x))^(-1/n) for n > 0.

a(n) = A385896(n + 6, 6).

gcd(a(n), a(n+1)) = 1.