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 A034265 #30 Sep 08 2022 08:44:51
%S A034265 1,13,76,300,930,2442,5676,12012,23595,43615,76648,129064,209508,
%T A034265 329460,503880,751944,1097877,1571889,2211220,3061300,4177030,5624190,
%U A034265 7480980,9839700,12808575,16513731,21101328,26739856,33622600,41970280
%N A034265 a(n) = binomial(n+6,6)*(6*n+7)/7.
%D A034265 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A034265 Vincenzo Librandi, <a href="/A034265/b034265.txt">Table of n, a(n) for n = 0..1000</a>
%H A034265 <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 A034265 G.f.: (1+5*x)/(1-x)^8.
%F A034265 a(0)=1, a(1)=13, a(2)=76, a(3)=300, a(4)=930, a(5)=2442, a(6)=5676, a(7)=12012, a(n) = 8*a(n-1) -28*a(n-2) +56*a(n-3) -70*a(n-4) +56*a(n-5) -28*a(n-6) +8*a(n-7) -a(n-8). - _Harvey P. Dale_, Jul 29 2014
%p A034265 seq((6*n+7)*binomial(n+6,6)/7, n=0..30); # _G. C. Greubel_, Aug 28 2019
%t A034265 Accumulate[Table[(n+1)Binomial[n+5,5],{n,0,30}]] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {1,13,76,300,930,2442,5676, 12012}, 30] (* _Harvey P. Dale_, Jul 29 2014 *)
%t A034265 CoefficientList[Series[(1+5x)/(1-x)^8, {x,0,40}], x] (* _Vincenzo Librandi_, Jul 30 2014 *)
%o A034265 (Magma) [(6*n+7)*Binomial(n+6,6)/7: n in [0..40]]; // _Vincenzo Librandi_, Jul 30 2014
%o A034265 (PARI) a(n)=(6*n/7+1)*binomial(n+6,6) \\ _Charles R Greathouse IV_, Oct 07 2015
%o A034265 (Sage) [(6*n+7)*binomial(n+6,6)/7 for n in (0..30)] # _G. C. Greubel_, Aug 28 2019
%o A034265 (GAP) List([0..30], n-> (6*n+7)*Binomial(n+6,6)/7); # _G. C. Greubel_, Aug 28 2019
%Y A034265 a(n)=f(n, 5) where f is given in A034261.
%Y A034265 Partial sums of A027810.
%Y A034265 Cf. A093563 ((6, 1) Pascal, column m=7).
%Y A034265 Cf. similar sequences listed in A254142.
%K A034265 nonn,easy
%O A034265 0,2
%A A034265 _Clark Kimberling_
%E A034265 Corrected and extended by _N. J. A. Sloane_, Apr 21 2000