A132756 a(n) = n*(n + 27)/2.

0, 14, 29, 45, 62, 80, 99, 119, 140, 162, 185, 209, 234, 260, 287, 315, 344, 374, 405, 437, 470, 504, 539, 575, 612, 650, 689, 729, 770, 812, 855, 899, 944, 990, 1037, 1085, 1134, 1184, 1235, 1287, 1340, 1394, 1449, 1505, 1562, 1620

Offset: 0

Author

Omar E. Pol, Aug 28 2007

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217, A001008, A002805, A056126, A132769.

Programs

Mathematica

Table[(n(n+27))/2,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,14,29},50] (* Harvey P. Dale, Apr 10 2022 *)

PARI

a(n)=n*(n+27)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

Let f(n,i,a) = Sum_{k=0..n-i} (binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j)), then a(n) = -f(n,n-1,14), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 13 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(n) = 14*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

From Chai Wah Wu, Jun 02 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.

G.f.: x*(13*x - 14)/(x - 1)^3. (End)

From Amiram Eldar, Jan 10 2021: (Start)

Sum_{n>=1} 1/a(n) = 2*A001008(27)/(27*A002805(27)) = 312536252003/1084231348200.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/27 - 57128792093/1084231348200. (End)

From Elmo R. Oliveira, Jan 12 2025: (Start)

E.g.f.: exp(x)*x*(28 + x)/2.

a(n) = A132769(n)/2. (End)