A132757 a(n) = n*(n+29)/2.

0, 15, 31, 48, 66, 85, 105, 126, 148, 171, 195, 220, 246, 273, 301, 330, 360, 391, 423, 456, 490, 525, 561, 598, 636, 675, 715, 756, 798, 841, 885, 930, 976, 1023, 1071, 1120, 1170, 1221, 1273, 1326, 1380, 1435, 1491, 1548, 1606, 1665

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

If we define 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-1,15), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = n + a(n-1) + 14 with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

From Colin Barker, Mar 18 2012: (Start)

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

G.f.: x*(15-14*x)/(1-x)^3. (End)

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

From Amiram Eldar, Jan 11 2021: (Start)

Sum_{n>=1} 1/a(n) = 2*A001008(29)/(29*A002805(29)) = 9227046511387/33771798660600.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/29 - 236266661971/4824542665800. (End)

Mathematica

i=-14; s=0; lst={}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 29 2008 *)

Prog

(PARI) a(n)=n*(n+29)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A001008, A002805, A056126.

Sequence in context: A125169 A044457 A249452 * A045135 A283122 A195046

Adjacent sequences: A132754 A132755 A132756 * A132758 A132759 A132760

Keyword

easy,nonn

Author

Omar E. Pol, Aug 28 2007

Status

approved