A218394 - OEIS

%I #11 Sep 19 2023 11:25:16

%S 1,5,7,11,25,27,31,35,37,51,55,57,61,125,127,131,135,137,151,155,157,

%T 161,175,177,181,185,187,251,255,257,261,275,277,281,285,287,301,305,

%U 307,311,625,627,631,635,637,651,655,657,661,675,677,681,685,687,751

%N Numbers such that sum(i<=n) binomial(n,i)*binomial(2*n-2*i, n-i) is not divisible by 5.

%C a(n) = A037453(2*n-1) (proved by Schur, see link).

%H W. Shur, <a href="https://doi.org/10.37236/1331">The last digit of C(2*n,n) and Sigma C(n,i)*C(2*n-2*i,n-i)</a>, The Electronic Journal of Combinatorics, #R16, Volume 4, Issue 2 (1997).

%F a(n)=2*n - 1 + 2*sum{i=1,n} 5^(i-1)*floor((2*n-1)/3^i).

%o (PARI) lista(nb) = {for (n=1, nb, if (sum(i=1,n, binomial(n, i)*binomial(2*n-2*i,n-i)) % 5 != 0, print1(n, ", ")););}

%o (PARI) a(n) = {2*n-1+2*sum(i=1,n, 5^(i-1)*floor((2*n-1)/3^i))}

%Y Cf. A037453.

%K nonn

%O 1,2

%A _Michel Marcus_, Oct 28 2012