This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253944 #59 Apr 06 2025 15:00:15
%S A253944 3,24,108,360,990,2376,5148,10296,19305,34320,58344,95472,151164,
%T A253944 232560,348840,511632,735471,1038312,1442100,1973400,2664090,3552120,
%U A253944 4682340,6107400,7888725,10097568,12816144,16138848,20173560,25043040,30886416,37860768
%N A253944 a(n) = 3*binomial(n+1,7).
%C A253944 For a set of integers {1,2,...,n}, a(n) is the sum of the 2 smallest elements of each subset with 6 elements, which is 3*C(n+1,7) (for n>=6), hence a(n) = 3*C(n+1,7) = 3*A000580(n+1).
%H A253944 G. C. Greubel, <a href="/A253944/b253944.txt">Table of n, a(n) for n = 6..1000</a>
%H A253944 Serhat Bulut and Oktay Erkan Temizkan, <a href="http://matematikproje.com/dosyalar/7e1cdSubset_smallest_elements_Sum.pdf">Subset Sum Problem</a>
%H A253944 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A253944 a(n) = 3*C(n+1,7) = 3*A000580(n+1).
%F A253944 a(n) = 3*C(n+1,7) = n*(n^6 - 14*n^5 + 70*n^4 - 140*n^3 + 49*n^2 + 154*n - 120)/1680.
%F A253944 From _G. C. Greubel_, Apr 03 2025: (Start)
%F A253944 G.f.: 3*x^6/(1-x)^8.
%F A253944 E.g.f.: (3/7!)*x^6*(x+7)*exp(x). (End)
%e A253944 For A={1,2,3,4,5,6,7}, subsets with 6 elements are {1,2,3,4,5,6}, {1,2,3,4,5,7}, {1,2,3,4,6,7}, {1,2,3,5,6,7}, {1,2,4,5,6,7}, {1,3,4,5,6,7}, {2,3,4,5,6,7}.
%e A253944 Sum of 2 smallest elements of each subset:
%e A253944 a(7) = (1+2)+(1+2)+(1+2)+(1+2)+(1+2)+(1+3)+(2+3) = 24 = 3*C(7+1,7) = 3*A000580(7+1).
%t A253944 Drop[Plus @@ Flatten[Part[#, 1 ;; 2] & /@ Subsets[Range@ #, {6}]] & /@
%t A253944 Range@ 28, 5] (* _Michael De Vlieger_, Jan 20 2015 *)
%t A253944 3 Binomial[Range[7, 29], 7] (* _Michael De Vlieger_, Feb 13 2015, after _Alonso del Arte_ at A253946 *)
%o A253944 (PARI) a(n)=3*binomial(n+1,7) \\ _Charles R Greathouse IV_, Feb 04 2015
%o A253944 (Magma) [3*Binomial(n+1, 7): n in [6..40]]; // _Vincenzo Librandi_, Feb 13 2015
%o A253944 (SageMath)
%o A253944 def A253944(n): return 3*binomial(n+1,7)
%o A253944 print([A253944(n) for n in range(6,51)]) # _G. C. Greubel_, Apr 03 2025
%Y A253944 Cf. A000580.
%K A253944 nonn,easy
%O A253944 6,1
%A A253944 _Serhat Bulut_, Jan 20 2015
%E A253944 More terms from _Vincenzo Librandi_, Feb 13 2015