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 A382503 #35 Apr 17 2025 14:54:34
%S A382503 1,4,11,39,127,476,1717,6474,24321,92508,352717,1352589,5200301,
%T A382503 20060020,77558897,300546669,1166803111,4537592436,17672631901,
%U A382503 68923356953,269128938947,1052049834580,4116715363801,16123803200574,63205303219003,247959271674356
%N A382503 a(n) = Sum_{d|n} binomial(2*d-1,d).
%F A382503 G.f.: Sum_{k>=1} binomial(2*k-1,k) * x^k / (1 - x^k).
%F A382503 a(n) = [(x*y)^n] Sum_{k>=1} x^k / (1 - x^k - y^k).
%F A382503 a(n) = Sum_{d|n} A088218(d).
%F A382503 a(n) = Sum_{d|n} A001700(d-1).
%F A382503 a(n) = Sum_{d|n} A045630(d) * A000005(n/d).
%F A382503 a(n) = A072929(n) / 2.
%t A382503 Table[Sum[Binomial[2 d - 1, d], {d, Divisors[n]}], {n, 1, 26}]
%t A382503 nmax = 26; CoefficientList[Series[Sum[Binomial[2 k - 1, k] x^k/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A382503 (PARI) a(n) = sumdiv(n, d, binomial(2*d-1,d)); \\ _Michel Marcus_, Apr 17 2025
%Y A382503 Cf. A000005, A000984, A001700, A045630, A072929, A088218.
%K A382503 nonn
%O A382503 1,2
%A A382503 _Ilya Gutkovskiy_, Apr 10 2025