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.

A329533 First differences of A051924, or second differences of Central binomial coefficients A000984.

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%I A329533 #11 Sep 13 2024 07:46:53
%S A329533 3,10,36,132,490,1836,6930,26312,100386,384540,1478048,5697720,
%T A329533 22019556,85284920,330961950,1286562960,5009003250,19528599420,
%U A329533 76231136520,297910080600,1165429743660,4563490674600,17884841191620,70148829799152,275344923755700,1081512966189656,4250730282412320
%N A329533 First differences of A051924, or second differences of Central binomial coefficients A000984.
%F A329533 a(n) = A051924(n) - A051924(n-1) = A000984(n+2) - 2*A000984(n+1) + A000984(n).
%F A329533 a(n) = 3*(3*n+2)*(n+1)*binomial(2*n+4,n+2)/(4*(2*n+1)*(2*n+3)). - _Alois P. Heinz_, Sep 13 2024
%t A329533 Differences[#, 2] &@ Array[Binomial[2 #, #] &, 29, 0] (* _Michael De Vlieger_, Nov 15 2019 *)
%o A329533 (PARI) C=vector(30,n,binomial(2*n--,n));C=C[^1]-C[^-1];C=C[^1]-C[^-1]
%Y A329533 Cf. A000984, A051924, A163771, A094796.
%K A329533 nonn
%O A329533 0,1
%A A329533 _M. F. Hasler_, Nov 15 2019