A081911 a(n) = 5^n*(n^2 - n + 50)/50.

1, 5, 26, 140, 775, 4375, 25000, 143750, 828125, 4765625, 27343750, 156250000, 888671875, 5029296875, 28320312500, 158691406250, 885009765625, 4913330078125, 27160644531250, 149536132812500, 820159912109375, 4482269287109375, 24414062500000000, 132560729980468750

Offset

0,2

Comments

Binomial transform of A081910 5th binomial transform of (1,0,1,0,0,0,...).

Case k=5 where a(n,k) = k^n*(n^2 - n + 2*k^2)/(2*k^2) with g.f. (1 - 2*k*x + (k^2+1)*x^2)/(1-k*x)^3.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..150

Index entries for linear recurrences with constant coefficients, signature (15,-75,125).

Formula

a(n) = 5^n*(n^2 - n + 50)/50.

G.f.: (1 - 10*x + 26*x^2)/(1-5*x)^3.

a(n) = 15*a(n-1) - 75*a(n-2) + 125*a(n-3); a(0)=1, a(1)=5, a(2)=26. - Harvey P. Dale, Jul 22 2011

E.g.f.: (1 + x^2/2)*exp(5*x). - Elmo R. Oliveira, Nov 12 2025

Mathematica

Table[5^n(n^2-n+50)/50, {n, 0, 20}] (* or *) LinearRecurrence[{15, -75, 125}, {1, 5, 26}, 20] (* Harvey P. Dale, Jul 22 2011 *)

Prog

(Magma) [5^n*(n^2-n+50)/50: n in [0..40]]; // Vincenzo Librandi, Apr 27 2011
(PARI) a(n)=5^n*(n^2-n+50)/50 \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Cf. A081910, A081912.

Sequence in context: A035029 A081569 A005573 * A081187 A182401 A363308

Adjacent sequences: A081908 A081909 A081910 * A081912 A081913 A081914

Keyword

easy,nonn

Author

Paul Barry, Mar 31 2003

Status

approved