%I #50 Jan 10 2021 11:19:20
%S 0,11,23,36,50,65,81,98,116,135,155,176,198,221,245,270,296,323,351,
%T 380,410,441,473,506,540,575,611,648,686,725,765,806,848,891,935,980,
%U 1026,1073,1121,1170,1220,1271,1323,1376,1430,1485,1541,1598,1656,1715,1775,1836
%N a(n) = 11 + (23*n)/2 + n^2/2.
%H Cecilia Rossiter, <a href="https://web.archive.org/web/20130515133733/http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n+1) = A000096(n) + 9*n = A056126(n) + 2*n. - _Zerinvary Lajos_, Oct 01 2006
%F a(n) = A126890(n+1,10) for n>8. - _Reinhard Zumkeller_, Dec 30 2006
%F G.f.: (11-10x)/(1-x)^3. - _R. J. Mathar_, Sep 09 2008
%F 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-1) = -f(n,n-1,11), for n>=1. - _Milan Janjic_, Dec 20 2008
%F a(n) = n + a(n-1) + 11 (with a(-1)=0). - _Vincenzo Librandi_, Nov 16 2010
%F a(n) = 11*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F a(-1)=0, a(0)=11, a(1)=23, a(n)=3*a(n-1)-3*a(n-2)+a (n-3). - _Harvey P. Dale_, May 01 2016
%F a(n+1) = n*(n + 21)/2. - _Wolfdieter Lang_, Oct 28 2020
%F From _Amiram Eldar_, Jan 10 2021: (Start)
%F Sum_{n>=0} 1/a(n) = 2*A001008(21)/(21*A002805(21)) = 18858053/54318264.
%F Sum_{n>=0} (-1)^n/a(n) = 4*log(2)/21 - 166770367/2444321880. (End)
%e G.f. = 11 + 23*x + 36*x^2 + 50*x^3 + 65*x^4 + 81*x^5 + 98*x^6 + 116*x^7 + ...
%t Join[{0},CoefficientList[Series[(11-10x)/(1-x)^3,{x,0,50}],x]] (* or *) LinearRecurrence[{3,-3,1},{0,11,23},60] (* _Harvey P. Dale_, May 01 2016 *)
%o (PARI) a(n)=11+(23*n)/2+n^2/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A000096, A001008, A002805, A056126, A001477, A051942.
%K easy,nonn
%O -1,2
%A Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
%E Edited by _N. J. A. Sloane_, Oct 07 2006