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.

A071735 Expansion of (1+x^3*C^3)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

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%I A071735 #12 Jul 25 2025 05:07:23
%S A071735 1,2,5,15,47,152,504,1705,5863,20436,72046,256462,920550,3328192,
%T A071735 12109270,44305245,162911415,601700700,2231255070,8304089970,
%U A071735 31007435970,116130446640,436137803400,1642112017338,6197239974582,23438771087272,88826989017004,337262603824860
%N A071735 Expansion of (1+x^3*C^3)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.
%F A071735 a(n) = (2*binomial(2*n+1,n)+5*binomial(2*n-2,n+1))/(n+2) for n>0. - _Tani Akinari_, Jul 24 2025
%o A071735 (Maxima) a(n):=if n=0 then 1 else (2*binomial(2*n+1,n)+5*binomial(2*n-2,n+1))/(n+2); makelist(a(n),n,0,20);  /* _Tani Akinari_, Jul 24 2025 */
%Y A071735 First differences of A000782.
%K A071735 nonn
%O A071735 0,2
%A A071735 _N. J. A. Sloane_, Jun 06 2002