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 A051880 #24 Sep 04 2025 01:54:05
%S A051880 1,15,75,245,630,1386,2730,4950,8415,13585,21021,31395,45500,64260,
%T A051880 88740,120156,159885,209475,270655,345345,435666,543950,672750,824850,
%U A051880 1003275,1211301,1452465,1730575,2049720,2414280,2828936,3298680,3828825,4425015,5093235
%N A051880 a(n) = binomial(n+4,4)*(2*n+1).
%C A051880 Old name was: Partial sums of A051799.
%D A051880 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%D A051880 Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pp. 1-16.
%H A051880 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A051880 a(n) = C(n+4, 4)*(2n+1).
%F A051880 G.f.: (1+9*x)/(1-x)^6.
%F A051880 From _Amiram Eldar_, Sep 04 2025: (Start)
%F A051880 Sum_{n>=0} 1/a(n) = 128*log(2)/35 - 152/105.
%F A051880 Sum_{n>=0} (-1)^n/a(n) = 32*Pi/35 + 596/105 - 384*log(2)/35. (End)
%t A051880 Nest[Accumulate[#]&,Table[n(n+1)(10n-7)/6,{n,0,50}],2] (* _Harvey P. Dale_, Nov 13 2013 *)
%Y A051880 Cf. A051799.
%Y A051880 Cf. A093645 ((10, 1) Pascal, column m=5).
%Y A051880 A diagonal of A280880.
%K A051880 easy,nonn,changed
%O A051880 0,2
%A A051880 _Barry E. Williams_, Dec 14 1999
%E A051880 Name changed by _Alois P. Heinz_, Jan 09 2017