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 A375218 #14 Oct 17 2024 10:04:36
%S A375218 1,0,2,2,3,12,7,36,41,84,186,230,612,852,1733,3198,5112,10628,16873,
%T A375218 32562,57463,99892,188103,319188,591982,1040076,1849352,3351304,
%U A375218 5854119,10610416,18707180,33370938,59618393,105291208,188572347,333462928,593859439,1055432400,1870161060
%N A375218 a(n) = Sum_{k=0..floor(n/2)} (k+1) * binomial(k,n-2*k)^2.
%F A375218 G.f.: (1-x^2-x^3)/((1-x^2-x^3)^2 - 4*x^5)^(3/2).
%F A375218 D-finite with recurrence 2*n*(2*n+1)*a(n) +3*(n-1)*(2*n-3)*a(n-1) +4*(-2*n^2-3*n+4)*a(n-2) +2*(-10*n^2+n+27)*a(n-3) +2*(-4*n^2+11*n+27)*a(n-4) +(-2*n^2-27*n-27)*a(n-5) +2*(-4*n^2+7*n+18)*a(n-6) +3*(2*n+3)*(n-1)*a(n-7)=0. - _R. J. Mathar_, Oct 17 2024
%o A375218 (PARI) a(n) = sum(k=0, n\2, (k+1)*binomial(k, n-2*k)^2);
%Y A375218 Cf. A182884, A375470.
%Y A375218 Cf. A298567.
%K A375218 nonn
%O A375218 0,3
%A A375218 _Seiichi Manyama_, Oct 17 2024