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 A370285 #10 Jan 04 2025 22:30:52
%S A370285 1,2,6,23,94,392,1659,7107,30734,133880,586576,2582142,11411371,
%T A370285 50597900,224986467,1002867878,4479814606,20049099908,89878609344,
%U A370285 403521966942,1814102538624,8165526187128,36794746597494,165968135843522,749314496125451,3385881647958442
%N A370285 Coefficient of x^n in the expansion of ( (1+x)^2 + x^3 )^n.
%F A370285 a(n) = Sum_{k=0..floor(n/3)} binomial(n,k) * binomial(2*n-2*k,n-3*k).
%F A370285 The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / ((1+x)^2 + x^3) ). See A369212.
%p A370285 a := n -> binomial(2*n, n) * hypergeom([(1-n)/3, (2-n)/3, -n/3], [1/2-n, n+1], 27/4):
%p A370285 seq(simplify(a(n)), n = 0..25); # _Peter Luschny_, Jan 04 2025
%o A370285 (PARI) a(n) = sum(k=0, n\3, binomial(n, k)*binomial(2*n-2*k, n-3*k));
%Y A370285 Cf. A006139, A026375, A369212.
%Y A370285 Similar to A082759.
%K A370285 nonn
%O A370285 0,2
%A A370285 _Seiichi Manyama_, Feb 14 2024