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 A377189 #10 Oct 19 2024 08:31:48
%S A377189 1,0,10,10,70,140,490,1260,3570,9660,25872,69300,182490,480480,
%T A377189 1252680,3255252,8412690,21655920,55535480,141921780,361577216,
%U A377189 918529040,2327337740,5882631040,14836032770,37339221192,93794645700,235186913780,588736957920,1471462327160
%N A377189 Expansion of 1/(1 - 4*x^2 - 4*x^3)^(5/2).
%F A377189 a(0) = 1, a(1) = 0, a(2) = 10; a(n) = (4*(n+3)*a(n-2) + 2*(2*n+9)*a(n-3))/n.
%F A377189 a(n) = Sum_{k=0..floor(n/2)} (-4)^k * binomial(-5/2,k) * binomial(k,n-2*k).
%o A377189 (PARI) a(n) = sum(k=0, n\2, (-4)^k*binomial(-5/2, k)*binomial(k, n-2*k));
%Y A377189 Cf. A115962, A377186, A377190.
%Y A377189 Cf. A374511.
%K A377189 nonn
%O A377189 0,3
%A A377189 _Seiichi Manyama_, Oct 19 2024