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 A178824 #24 Mar 26 2025 05:54:02
%S A178824 1,1,6,41,362,3542,37692,424377,4990722,60704138,758665388,9694652838,
%T A178824 126203947828,1668947978908,22370427181624,303383342784729,
%U A178824 4156846359584754,57473870722327874,801081711581734764,11246487794657694810,158920231643036635860,2258896576436091238860
%N A178824 a(n) = Sum_{k=0..n} binomial(n,k)^4/(n+1).
%H A178824 G. C. Greubel, <a href="/A178824/b178824.txt">Table of n, a(n) for n = 0..830</a>
%F A178824 a(n) = A005260(n)/(n+1).
%F A178824 a(n) = Sum_{k=0..n} binomial(n,k)^2 * ( binomial(n,k) - binomial(n,k-1) )^2. - _Seiichi Manyama_, Mar 26 2025
%F A178824 a(n) ~ 2^(4*n + 1/2) / (Pi^(3/2) * n^(5/2)). - _Vaclav Kotesovec_, Mar 26 2025
%p A178824 a:=n->add(binomial(n,k)^4/(n+1),k=0..n): seq(a(n),n=0..20); # _Muniru A Asiru_, Jan 22 2019
%t A178824 Table[Sum[Binomial[n,k]^4/(n+1), {k,0,n}], {n,0,20}] (* _G. C. Greubel_, Jan 22 2019 *)
%o A178824 (PARI) {a(n)=sum(k=0, n, binomial(n, k)^4)/(n+1)}
%o A178824 (Magma) [(&+[Binomial(n,k)^4/(n+1): k in [0..n]]): n in [0..20]]; // _G. C. Greubel_, Jan 22 2019
%o A178824 (Sage) [sum(binomial(n,k)^4/(n+1) for k in (0..n)) for n in (0..20)] # _G. C. Greubel_, Jan 22 2019
%o A178824 (GAP) List([0..20], n-> Sum([0..n], k-> Binomial(n,k)^4/(n+1) )); # _G. C. Greubel_, Jan 22 2019
%Y A178824 Cf. A000108, A005260, A131428.
%K A178824 nonn
%O A178824 0,3
%A A178824 _Paul D. Hanna_, Dec 27 2010