A346007 - OEIS

%I #14 Jul 27 2021 06:23:30

%S 0,1,5,10,10,5,32,80,80,40,10,243,405,270,90,15,1024,1280,640,160,20,

%T 3125,3125,1250,250,25,7776,6480,2160,360,30,16807,12005,3430,490,35,

%U 32768,20480,5120,640,40,59049,32805,7290,810,45,100000,50000,10000,1000,50

%N 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 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 J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. See pp. 63-64.

%p f:=proc(n,b) local i;

%p for i from 0 to b-1 do

%p if ((n+i) mod b) = 0 then return(binomial(b,i+1)*((n+i)/b)^(i+1)); fi;

%p od;

%p end;

%p [seq(f(n,5),n=0..80)];

%o (Python)

%o from sympy import binomial

%o def A346007(n):

%o     i = (5-n)%5

%o     return binomial(5,i+1)*((n+i)//5)**(i+1) # _Chai Wah Wu_, Jul 25 2021

%Y Setting b = 2, 3, or 4 gives A346004, A346005, and A346006.

%Y Cf. A125714, A346595.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Jul 25 2021