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.

A371827 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-2*k,n-3*k).

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%I A371827 #11 Aug 10 2024 15:59:03
%S A371827 1,2,6,23,94,392,1680,7387,33110,150905,698996,3287550,15685420,
%T A371827 75877427,371994692,1847450970,9290557158,47291312897,243574276884,
%U A371827 1268915237141,6683909556420,35585631836229,191433293140656,1040197718292138,5707318227692796
%N A371827 a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-2*k,n-3*k).
%F A371827 a(n) = [x^n] 1/((1-x-n*x^3) * (1-x)^n).
%F A371827 a(n) ~ exp(4*n^(2/3)/3 + 2*n^(1/3)/9) * n^(n/3) / 3. - _Vaclav Kotesovec_, Apr 07 2024
%t A371827 Join[{1},Table[Sum[n^k Binomial[2n-2k,n-3k],{k,0,Floor[n/3]}],{n,30}]] (* _Harvey P. Dale_, Aug 10 2024 *)
%o A371827 (PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-2*k, n-3*k));
%Y A371827 Cf. A371825, A371826.
%Y A371827 Cf. A368891.
%K A371827 nonn
%O A371827 0,2
%A A371827 _Seiichi Manyama_, Apr 07 2024