A379745 a(n) = Sum_{k=1..n-1} binomial(n,k)*2^(n-k-1)*(k-1).

0, 0, 3, 20, 95, 394, 1519, 5592, 19935, 69398, 237215, 799204, 2661295, 8776962, 28714191, 93300656, 301392575, 968682286, 3099626047, 9879746748, 31382108175, 99375452570, 313814790383, 988511766280, 3106741678495, 9743852563014, 30502457048799, 95320102780052, 297398570349935, 926510631296818, 2882476923066895, 8956266393600864, 27795307127744895, 86165447371545182, 266834924374534271

Offset

1,3

Links

Table of n, a(n) for n=1..35.

Index entries for linear recurrences with constant coefficients, signature (10,-38,68,-57,18).

Formula

a(n) = (3^(n-1) - 1)*(n-3)/2 + 2^(n-1) - 1.

From Elmo R. Oliveira, Jul 05 2026: (Start)

G.f.: x^3*(3 - 10*x + 9*x^2) / ((1 - x)^2 * (1 - 2*x) * (1 - 3*x)^2).

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

a(n) = 10*a(n-1) - 38*a(n-2) + 68*a(n-3) - 57*a(n-4) + 18*a(n-5) for n > 5. (End)

Mathematica

LinearRecurrence[{10, -38, 68, -57, 18}, {0, 0, 3, 20, 95}, 35] (* James C. McMahon, Jan 07 2025 *)

Crossrefs

Sequence in context: A015529 A278319 A305203 * A246150 A000948 A074831

Adjacent sequences: A379742 A379743 A379744 * A379746 A379747 A379748

Keyword

nonn,easy,changed

Author

Ocean Wong, Jan 01 2025

Status

approved