simplify_sum produces incorrect hypergeometric answer

Imported from SourceForge on 2024-07-06 18:07:19 Created by dimpase on 2024-02-15 00:26:58 Original: https://sourceforge.net/p/maxima/bugs/4262

(%i4) load("simplify_sum");
(%o4) "/usr/share/maxima/5.45.1/share/solve_rec/simplify_sum.mac"

(%i5) sum(1/factorial(n^2), n, 1, inf), simpsum;
(%o5) 'sum(1/(n^2)!,n,1,inf)

(%i6) simplify_sum(%);
1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
1/'product(n^2+%,%,1,2*n+1) non-rational term ratio to nusum
(%o6) %f[1,4]([1],[1-%i,%i+1,1-sqrt(2)*%i,sqrt(2)*%i+1],1)

sum(1/factorial(n^2),n,1,oo) is obviously not a hypergeometric function, and it can be confirmed by a numerical check. See e.g. https://mathoverflow.net/questions/463964/factorial-series-jd-sum-n-1-infty-frac1nd-and-hypergeometric-fu and https://groups.google.com/g/sage-devel/c/E-JooEu5QTo/m/Zgo3igb-AAAJ

rtoy / maxima

simplify_sum produces incorrect hypergeometric answer #2684