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A132754 a(n) = n*(n + 23)/2.

%I A132754 #43 Nov 29 2024 20:39:13
%S A132754 0,12,25,39,54,70,87,105,124,144,165,187,210,234,259,285,312,340,369,
%T A132754 399,430,462,495,529,564,600,637,675,714,754,795,837,880,924,969,1015,
%U A132754 1062,1110,1159,1209,1260,1312,1365,1419,1474,1530
%N A132754 a(n) = n*(n + 23)/2.
%H A132754 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132754 a(n) = n*(n + 23)/2.
%F A132754 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-1,12), for n>=1. - _Milan Janjic_, Dec 20 2008
%F A132754 a(n) = n + a(n-1) + 11, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A132754 a(0)=0, a(1)=12, a(2)=25, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Jun 21 2011
%F A132754 a(n) = 12*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F A132754 From _Amiram Eldar_, Jan 10 2021: (Start)
%F A132754 Sum_{n>=1} 1/a(n) = 2*A001008(23)/(23*A002805(23)) = 444316699/1368302936.
%F A132754 Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/23 - 3825136961/61573632120. (End)
%F A132754 From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F A132754 G.f.: x*(11*x - 12)/(x-1)^3.
%F A132754 E.g.f.: exp(x)*x*(24 + x)/2.
%F A132754 a(n) = A132765(n)/2. (End)
%t A132754 Table[n (n + 23)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 12, 25}, 50] (* _Harvey P. Dale_, Jun 21 2011 *)
%o A132754 (PARI) a(n)=n*(n+23)/2 \\ _Charles R Greathouse IV_, Jun 16 2017
%Y A132754 Cf. A000217, A001008, A002805, A056126, A132765.
%K A132754 nonn,easy
%O A132754 0,2
%A A132754 _Omar E. Pol_, Aug 28 2007