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 A051947 #26 Nov 08 2024 10:24:29
%S A051947 1,10,49,168,462,1092,2310,4488,8151,14014,23023,36400,55692,82824,
%T A051947 120156,170544,237405,324786,437437,580888,761530,986700,1264770,
%U A051947 1605240,2018835,2517606,3115035,3826144,4667608,5657872,6817272,8168160,9735033,11544666
%N A051947 Partial sums of A034263.
%D A051947 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A051947 Harvey P. Dale, <a href="/A051947/b051947.txt">Table of n, a(n) for n = 0..1000</a>
%H A051947 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A051947 a(n) = C(n+5, 5)*(2n+3)/3.
%F A051947 G.f.: (1+3*x)/(1-x)^7.
%F A051947 From _Amiram Eldar_, Feb 15 2022: (Start)
%F A051947 Sum_{n>=0} 1/a(n) = 2161/28 - 768*log(2)/7.
%F A051947 Sum_{n>=0} (-1)^n/a(n) = 192*Pi/7 - 624*log(2)/7 - 657/28. (End)
%t A051947 Nest[Accumulate,Range[1,160,4],5] (* _Vladimir Joseph Stephan Orlovsky_, Jan 29 2012 *)
%t A051947 LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,10,49,168,462,1092,2310},40] (* _Harvey P. Dale_, Nov 08 2024 *)
%Y A051947 Cf. A034263.
%Y A051947 Cf. A093561 ((4, 1) Pascal, column m=6).
%K A051947 easy,nonn
%O A051947 0,2
%A A051947 _Barry E. Williams_, Dec 21 1999
%E A051947 Corrected by _T. D. Noe_, Nov 09 2006