A132755 a(n) = n*(n + 25)/2.

0, 13, 27, 42, 58, 75, 93, 112, 132, 153, 175, 198, 222, 247, 273, 300, 328, 357, 387, 418, 450, 483, 517, 552, 588, 625, 663, 702, 742, 783, 825, 868, 912, 957, 1003, 1050, 1098, 1147, 1197, 1248, 1300, 1353, 1407, 1462, 1518, 1575

Offset

0,2

Links

Table of n, a(n) for n=0..45.

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

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, 13), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 12 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(n) = 13*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

a(0)=0, a(1)=13, a(2)=27; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Aug 09 2014

From Amiram Eldar, Jan 10 2021: (Start)

Sum_{n>=1} 1/a(n) = 2*A001008(25)/(25*A002805(25)) = 34052522467/111546435000.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/25 - 19081066231/334639305000. (End)

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: x*(12*x - 13)/(x-1)^3.

E.g.f.: exp(x)*x*(26 + x)/2.

a(n) = A132767(n)/2. (End)

Mathematica

Table[(n(n+25))/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 13, 27}, 50] (* Harvey P. Dale, Aug 09 2014 *)

Prog

(Magma) [n*(n + 25)/2 : n in [0..50]]; // Wesley Ivan Hurt, Jan 23 2017
(PARI) a(n)=n*(n+25)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A001008, A002805, A056126, A132767.

Sequence in context: A136773 A358053 A189528 * A250667 A147450 A195045

Adjacent sequences: A132752 A132753 A132754 * A132756 A132757 A132758

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved