cp's OEIS Frontend

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.

A050484 Partial sums of A051946.

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%I A050484 #21 Sep 08 2022 08:44:58
%S A050484 1,12,68,264,810,2112,4884,10296,20163,37180,65208,109616,177684,
%T A050484 279072,426360,635664,927333,1326732,1865116,2580600,3519230,4736160,
%U A050484 6296940,8278920,10772775,13884156,17735472,22467808,28242984,35245760
%N A050484 Partial sums of A051946.
%D A050484 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A050484 Vincenzo Librandi, <a href="/A050484/b050484.txt">Table of n, a(n) for n = 0..1000</a>
%H A050484 <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 A050484 a(n) = C(n+6, 6)*(5n+7)/7.
%F A050484 G.f.: (1+4*x)/(1-x)^8.
%t A050484 CoefficientList[Series[(1 + 4 x)/(1 - x)^8, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jul 30 2014 *)
%t A050484 Accumulate[CoefficientList[Series[(1+4x)/(1-x)^7,{x,0,40}],x]] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,12,68,264,810,2112,4884,10296},30] (* _Harvey P. Dale_, Aug 21 2020 *)
%o A050484 (Magma) [((5*n+7)*Binomial(n+6,6))/7: n in [0..60]]; // _Vincenzo Librandi_, Jul 30 2014
%o A050484 (PARI) a(n)=binomial(n+6, 6)*(5*n+7)/7 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A050484 Cf. A051946, A093562 ((5, 1) Pascal, column m=7).
%K A050484 easy,nonn
%O A050484 0,2
%A A050484 _Barry E. Williams_, Dec 26 1999