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 A136046 #17 Jun 30 2025 23:42:55
%S A136046 1,3,26,345,5754,110586,2341548,53208441,1276027610,31930139670,
%T A136046 826963069140,22035414489270,601361536493340,16749316314679500,
%U A136046 474777481850283240,13665774112508864385,398682239947705700730,11770712453752716494910,351240103372615793928900,10581780543413346794758770
%N A136046 Bisection of A138543.
%F A136046 a(n) = Sum_{k=0..2*n} (-1)^k*binomial(2*n, k)*A005558(k)*A001405(2*n-k). - _Mélika Tebni_, Jun 30 2025
%t A136046 Q2[n_] := Quotient[n, 2];
%t A136046 A136046[n_] := Sum[(-1)^k*Binomial[2n, k] CatalanNumber[Q2[k+1]] CatalanNumber[Q2[k]](2*Q2[k]+1) Binomial[2n-k, Q2[2*n-k]], {k, 0, 2n + 1}];
%t A136046 Array[A136046, 20, 0] (* After _Mélika Tebni_, _Peter Luschny_, Jun 30 2025 *)
%o A136046 (Python)
%o A136046 from math import comb as C
%o A136046 def CN(n): return (C(2*n, n)//(n+1)) # Catalan numbers
%o A136046 def a(n): return sum((-1)**k*C(2*n, k)*CN((k+1)//2)*CN(k//2)*(2*(k//2)+1)*C(2*n-k, (2*n-k)//2) for k in range(2*n+1)) # _Mélika Tebni_, Jun 30 2025
%Y A136046 Cf. A001405, A005558, A138543.
%K A136046 nonn
%O A136046 0,2
%A A136046 _N. J. A. Sloane_, Mar 25 2008
%E A136046 a(16)-a(19) from _Mélika Tebni_, Jun 30 2025