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A056121 a(n) = n*(n + 15)/2.

%I A056121 #55 Jul 02 2025 16:02:00
%S A056121 0,8,17,27,38,50,63,77,92,108,125,143,162,182,203,225,248,272,297,323,
%T A056121 350,378,407,437,468,500,533,567,602,638,675,713,752,792,833,875,918,
%U A056121 962,1007,1053,1100,1148,1197,1247,1298,1350,1403,1457,1512,1568,1625
%N A056121 a(n) = n*(n + 15)/2.
%H A056121 G. C. Greubel, <a href="/A056121/b056121.txt">Table of n, a(n) for n = 0..1000</a>
%H A056121 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A056121 G.f.: x*(8-7*x)/(1-x)^3.
%F A056121 a(n) = A000096(n) + 6*n = A056119(n) + n = A056126(n) - n. - _Zerinvary Lajos_, Oct 01 2006
%F A056121 a(n-15) = binomial(n,2) - 7*n. - _Zerinvary Lajos_, Nov 26 2006
%F A056121 a(n) = A126890(n,7) for n>6. - _Reinhard Zumkeller_, Dec 30 2006
%F A056121 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-1,8), for n>=1. - _Milan Janjic_, Dec 20 2008
%F A056121 a(n) = a(n-1)+ n + 7 (with a(0)=0). - _Vincenzo Librandi_, Aug 07 2010
%F A056121 Sum_{n>=1} 1/a(n) = 1195757/2702700 via A132760. - _R. J. Mathar_, Jul 14 2012
%F A056121 a(n) = 8*n - floor(n/2) + floor(n^2/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F A056121 E.g.f.: x*(16 + x)*exp(x)/2. - _G. C. Greubel_, Jan 18 2020
%F A056121 Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/15 - 52279/540540. - _Amiram Eldar_, Jan 10 2021
%p A056121 a:=n->n*(n+15)/2: seq(a(n),n=0..60);
%t A056121 Table[n*(n + 15)/2, {n, 0, 100}] (* _Paolo Xausa_, Aug 02 2024 *)
%o A056121 (PARI) a(n)=n*(n+15)/2 \\ _Charles R Greathouse IV_, Sep 24 2015
%o A056121 (Magma) [n*(n+15)/2: n in [0..60]]; // _G. C. Greubel_, Jan 18 2020
%o A056121 (Sage) [n*(n+15)/2 for n in (0..60)] # _G. C. Greubel_, Jan 18 2020
%o A056121 (GAP) List([0..60], n-> n*(n+15)/2 ); # _G. C. Greubel_, Jan 18 2020
%Y A056121 Cf. A000096, A001477, A056000, A056119, A056126.
%K A056121 easy,nonn
%O A056121 0,2
%A A056121 _Barry E. Williams_, Jul 06 2000
%E A056121 More terms from _James Sellers_, Jul 07 2000