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 A056001 #36 Mar 23 2025 23:40:20
%S A056001 1,16,108,480,1650,4752,12012,27456,57915,114400,213928,381888,655044,
%T A056001 1085280,1744200,2728704,4167669,6229872,9133300,13156000,18648630,
%U A056001 26048880,35897940,48859200,65739375,87512256,115345296,150629248,195011080,250430400,319159632
%N A056001 a(n) = (n+1)*binomial(n+7, 7).
%C A056001 Original name: A second-order recursive sequence.
%D A056001 Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A056001 Reinhard Zumkeller, <a href="/A056001/b056001.txt">Table of n, a(n) for n = 0..10000</a>
%H A056001 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A056001 G.f.: (1+7*x)/(1-x)^9.
%F A056001 a(n) = A245334(n+7,7)/A000142(7). - _Reinhard Zumkeller_, Aug 31 2014
%F A056001 a(n) = A000581(n+8)+7*A000581(n+7). - _R. J. Mathar_, Oct 24 2014
%F A056001 E.g.f.: (5040 +75600*x +194040*x^2 +170520*x^3 +66150*x^4 +12642*x^5 + 1225*x^6 +57*x^7 +x^8)*exp(x)/5040. - _G. C. Greubel_, Aug 29 2019
%F A056001 From _Amiram Eldar_, Jan 15 2023: (Start)
%F A056001 Sum_{n>=0} 1/a(n) = 7*Pi^2/6 - 37583/3600.
%F A056001 Sum_{n>=0} (-1)^n/a(n) = 7*Pi^2/12 - 2912*log(2)/15 + 155701/1200. (End)
%p A056001 seq((n+1)*binomial(n+7,7), n=0..30); # _G. C. Greubel_, Aug 29 2019
%t A056001 Table[(n+1)Binomial[n+7, 7], {n,0,30}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 19 2011; corrected by _Bruno Berselli_, Jan 23 2015 *)
%o A056001 (Haskell)
%o A056001 a056001 n = (n + 1) * a007318' (n + 7) 7
%o A056001 -- _Reinhard Zumkeller_, Aug 31 2014
%o A056001 (PARI) vector(30, n, n*binomial(n+6,7)) \\ _G. C. Greubel_, Aug 29 2019
%o A056001 (Magma) [(n+1)*Binomial(n+7,7): n in [0..30]]; // _G. C. Greubel_, Aug 29 2019
%o A056001 (Sage) [(n+1)*binomial(n+7,7) for n in (0..30)] # _G. C. Greubel_, Aug 29 2019
%o A056001 (GAP) List([0..30], n-> (n+1)*Binomial(n+7,7)); # _G. C. Greubel_, Aug 29 2019
%Y A056001 Partial sums of A052226.
%Y A056001 Cf. A093565 ((8, 1) Pascal, column m=8).
%Y A056001 Cf. A007318, A000142, A245334.
%K A056001 nonn,easy
%O A056001 0,2
%A A056001 _Barry E. Williams_, Jun 18 2000