A091433 a(n) = 2*3^n - 18*4^n + 24*5^n.

8, 54, 330, 1902, 10554, 57054, 302730, 1584462, 8208474, 42195774, 215618730, 1096731822, 5558447994, 28092104094, 141662102730, 713123219982, 3584886057114, 18001567510014, 90316558634730, 452818194072942, 2269034123643834, 11364947880381534, 56903862397694730

Offset

0,1

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (12,-47,60).

Formula

a(n) = Sum_{i=2..n+2} i!*i^2*Stirling2(n,i-2)*(-1)^(n+2-i).

From Elmo R. Oliveira, May 08 2026: (Start)

G.f.: 2*(4 - 21*x + 29*x^2)/((1-3*x)*(1-4*x)*(1-5*x)).

E.g.f.: 2*exp(3*x)*(1 - 9*exp(x) + 12*exp(2*x)).

a(n) = 12*a(n-1) - 47*a(n-2) + 60*a(n-3). (End)

Mathematica

Table[2*3^n - 18*4^n + 24*5^n, {n, 0, 25}]
(* Alternative: *)
LinearRecurrence[{12, -47, 60}, {8, 54, 330}, 25] (* Harvey P. Dale, Feb 14 2026 *)

Crossrefs

Sequence in context: A152692 A351845 A037966 * A081899 A057970 A208310

Adjacent sequences: A091430 A091431 A091432 * A091434 A091435 A091436

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Jan 08 2004

Extensions

More terms from Elmo R. Oliveira, May 08 2026

Status

approved