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 A383930 #7 May 16 2025 07:29:54
%S A383930 1,1,1020,14152314,1071646712640,286802348769420190,
%T A383930 209974096349134108992000,355016116241074708829385321492,
%U A383930 1228958111984894631846657261766656000,7960240318398277162915923478914410838135990,89961580311571094335785117669395413813764096000000
%N A383930 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n, k) * (n-k)^(5*n).
%C A383930 In general, for m>2, Sum_{k=0..n} (-1)^(n-k) * binomial(2*n, n-k) * k^(m*n) ~ 2^(2*n + 1/2) * r^(m*n + 1) * n^(m*n) / (sqrt(m + (2-m)*r^2) * exp(m*n) * (r^2 - 1)^n), where r is the root of the equation (1 + r)/(1 - r) = -exp(m/r).
%F A383930 a(n) ~ 2^(2*n + 1/2) * r^(5*n + 1) * n^(5*n) / (sqrt(5 - 3*r^2) * exp(5*n) * (r^2 - 1)^n), where r = 1.0145858159274292356581282820876562174881159476120290450838... is the root of the equation (1 + r)/(1 - r) = -exp(5/r).
%t A383930 Join[{1}, Table[Sum[(-1)^(n-k)*Binomial[2*n, n-k]*k^(5*n), {k, 0, n}], {n, 1, 12}]]
%Y A383930 Cf. A002674 (m=2), A383929 (m=3), A298851*A002674 (m=4).
%Y A383930 Cf. A383917.
%K A383930 nonn
%O A383930 0,3
%A A383930 _Vaclav Kotesovec_, May 15 2025