A027476 Third column of A027467.

1, 45, 1350, 33750, 759375, 15946875, 318937500, 6150937500, 115330078125, 2114384765625, 38058925781250, 674680957031250, 11806916748046875, 204350482177734375, 3503151123046875000, 59553569091796875000

Offset: 3

Author

Olivier Gérard

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 3..200
• Index entries for linear recurrences with constant coefficients, signature (45,-675,3375).

Crossrefs

Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), A081142 (q=12), this sequence (q=15).

Programs

Magma

[(n-1)*(n-2)/2 * 15^(n-3): n in [3..20]]; // Vincenzo Librandi, Dec 29 2012

Maple

seq((15)^(n-3)*binomial(n-1, 2), n=3..30) # G. C. Greubel, May 13 2021

Mathematica

Table[(n-1)*(n-2)/2 * 15^(n-3), {n, 3, 30}] (* Vincenzo Librandi, Dec 29 2012 *)

Sage

[(15)^(n-3)*binomial(n-1,2) for n in (3..30)] # G. C. Greubel, May 13 2021

Formula

Numerators of sequence a[3,n] in (a[i,j])^4 where a[i,j] = binomial(i-1, j-1)/2^(i-1) if j<=i, 0 if j>i.

a(n) = 15^(n-3)*binomial(n-1, 2).

From G. C. Greubel, May 13 2021: (Start)

a(n) = 45*a(n-1) - 675*a(n-2) + 3375*a(n-3).

G.f.: x^3/(1 - 15*x)^3.

E.g.f.: (-2 + (2 - 30*x + 225*x^2)*exp(15*x))/6750. (End)

From Amiram Eldar, Jan 06 2022: (Start)

Sum_{n>=3} 1/a(n) = 30 - 420*log(15/14).

Sum_{n>=3} (-1)^(n+1)/a(n) = 480*log(16/15) - 30. (End)