A027476 Third column of A027467.

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

Offset

3,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 3..200

Index entries for linear recurrences with constant coefficients, signature (45,-675,3375).

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)

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 *)

Prog

(Magma) [(n-1)*(n-2)/2 * 15^(n-3): n in [3..20]]; // Vincenzo Librandi, Dec 29 2012
(Sage) [(15)^(n-3)*binomial(n-1, 2) for n in (3..30)] # G. C. Greubel, May 13 2021

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).

Sequence in context: A346324 A243570 A145151 * A062262 A137716 A035521

Adjacent sequences: A027473 A027474 A027475 * A027477 A027478 A027479

Keyword

nonn

Author

Olivier Gérard

Status

approved