A025930 Expansion of 1/((1-2*x)*(1-3*x)*(1-5*x)*(1-6*x)).

1, 16, 165, 1400, 10661, 75936, 517525, 3421000, 22124421, 140796656, 885205685, 5513890200, 34098207781, 209668346176, 1283419890645, 7827611393000, 47601257612741, 288785879108496, 1748608103548405, 10571116251513400, 63824046118451301, 384931051134427616, 2319520273059954965

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (16,-91,216,-180).

Formula

From Vincenzo Librandi, Mar 19 2011: (Start)

a(n) = 16*a(n-1) - 91*a(n-2) + 216*a(n-3) - 180*a(n-4), n >= 4.

a(n) = 11*a(n-1) - 30*a(n-2) + 3^(n+1) - 2^(n+1), n >= 2. (End)

a(n) = 3*6^(n+1) - 5^(n+3)/6 + 3^(n+2)/2 - 2^(n+1)/3. - R. J. Mathar, Mar 19 2011

E.g.f.: exp(2*x)*(108*exp(4*x) - 125*exp(3*x) + 27*exp(x) - 4)/6. - Stefano Spezia, Apr 19 2026

Mathematica

a[0]=1; a[1]=16; a[n_]:=a[n]=3^(n+1)-2^(n+1)+11 a[n-1]-30 a[n-2]; Table[a[n], {n, 0, 22}] (* Vincenzo Librandi, Apr 18 2026 *)

Prog

(Magma) I:=[1, 16]; [n le 2 select I[n] else 3^n-2^n+11*Self(n-1)-30*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Apr 18 2026

Crossrefs

Sequence in context: A204031 A341084 A387273 * A125404 A246057 A265598

Adjacent sequences: A025927 A025928 A025929 * A025931 A025932 A025933

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Apr 18 2026

Status

approved