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%I #39 Jan 10 2021 02:48:43
%S 0,12,25,39,54,70,87,105,124,144,165,187,210,234,259,285,312,340,369,
%T 399,430,462,495,529,564,600,637,675,714,754,795,837,880,924,969,1015,
%U 1062,1110,1159,1209,1260,1312,1365,1419,1474,1530
%N a(n) = n*(n + 23)/2.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n*(n+23)/2.
%F 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 a(n) = n + a(n-1) + 11, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F 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 a(n) = 12*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F From _Amiram Eldar_, Jan 10 2021: (Start)
%F Sum_{n>=1} 1/a(n) = 2*A001008(23)/(23*A002805(23)) = 444316699/1368302936.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/23 - 3825136961/61573632120. (End)
%t Table[n (n + 23)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 12, 25}, 50] (* _Harvey P. Dale_, Jun 21 2011 *)
%o (PARI) a(n)=n*(n+23)/2 \\ _Charles R Greathouse IV_, Jun 16 2017
%Y Cf. A000217, A001008, A002805, A056126.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Aug 28 2007
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