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 A075878 #15 Apr 21 2025 03:20:51
%S A075878 4,40,544,8320,131584,2099200,33562624,536903680,8590065664,
%T A075878 137439477760,2199025352704,35184380477440,562949986975744,
%U A075878 9007199388958720,144115188612726784,2305843011361177600,36893488156009037824,590295810393065390080,9444732965876729380864,151115727452378402652160,2417851639231457372667904
%N A075878 Sum of coefficients of (x1)^(2i(1))*(x2)^(2i(2))*(x3)^(2i(3))*(x4)^(2i(4)) for {(i1),(i2),(i3),(i4)}=0,1,2,... : sum(i)=2n in the expansion of (x1+x2+x3+x4)^(2n) where n >= 1.
%C A075878 For k=3, the sequence divided by 3 is equal to A066443.
%F A075878 a(n, 4) = 2^(1-4)*Sum_{r=0..floor((4-1)/2)} binomial(4, r)*(4-2*r)^(2*n).
%F A075878 a(n, k) = 2^(1-k)*Sum_{r=0..floor((k-1)/2)} binomial(k, r)*(k-2*r)^(2*n) for k>=1.
%o A075878 (PARI) a(n, k=4) = 2^(1-k)*sum(r=0,floor((k-1)/2), binomial(k, r)*(k-2*r)^(2*n));
%o A075878 vector(33,n,a(n)) \\ _Joerg Arndt_, Apr 21 2025
%Y A075878 Cf. A066443.
%Y A075878 Essentially the same as A092812. - Kang Seonghoon (lifthrasiir(AT)gmail.com), Oct 09 2008
%K A075878 easy,nonn
%O A075878 1,1
%A A075878 Jan Hagberg (jan.hagberg(AT)stat.su.se), Oct 16 2002
%E A075878 Corrected by _T. D. Noe_, Nov 07 2006