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A346007 Let b=5. If n == -i (mod b) for 0 <= i < b, then a(n) = binomial(b,i+1)*((n+i)/b)^(i+1).

%I A346007 #14 Jul 27 2021 06:23:30
%S A346007 0,1,5,10,10,5,32,80,80,40,10,243,405,270,90,15,1024,1280,640,160,20,
%T A346007 3125,3125,1250,250,25,7776,6480,2160,360,30,16807,12005,3430,490,35,
%U A346007 32768,20480,5120,640,40,59049,32805,7290,810,45,100000,50000,10000,1000,50
%N A346007 Let b=5. If n == -i (mod b) for 0 <= i < b, then a(n) = binomial(b,i+1)*((n+i)/b)^(i+1).
%C A346007 These are the numbers that would arise if the Moessner construction on page 64 of Conway-Guy's "Book of Numbers" were extended to the fifth powers.
%D A346007 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. See pp. 63-64.
%p A346007 f:=proc(n,b) local i;
%p A346007 for i from 0 to b-1 do
%p A346007 if ((n+i) mod b) = 0 then return(binomial(b,i+1)*((n+i)/b)^(i+1)); fi;
%p A346007 od;
%p A346007 end;
%p A346007 [seq(f(n,5),n=0..80)];
%o A346007 (Python)
%o A346007 from sympy import binomial
%o A346007 def A346007(n):
%o A346007     i = (5-n)%5
%o A346007     return binomial(5,i+1)*((n+i)//5)**(i+1) # _Chai Wah Wu_, Jul 25 2021
%Y A346007 Setting b = 2, 3, or 4 gives A346004, A346005, and A346006.
%Y A346007 Cf. A125714, A346595.
%K A346007 nonn
%O A346007 0,3
%A A346007 _N. J. A. Sloane_, Jul 25 2021