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A051556
a(n) = number of 0<=k<=n such that n+k divides binomial(n,k).
2
1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 6, 3, 1, 2, 2, 1, 3, 2, 3, 6, 2, 3, 5, 5, 2, 3, 6, 4, 6, 5, 10, 12, 6, 4, 10, 8, 3, 8, 5, 8, 5, 3, 5, 11, 4, 4, 10, 7, 8, 9, 19, 21, 12, 8, 7, 8, 4, 3, 17, 13, 19, 23, 10, 11, 13, 16, 18, 14, 9, 11, 19, 13, 9, 16, 16, 25, 21, 17, 15, 18, 13, 16, 17, 19
OFFSET
1,9
LINKS
EXAMPLE
For n=9, 0<=k<=n, n+k divides C(n,k) only when k=3 and k=5, so a(9)=2.
MAPLE
f:= proc(n)
nops(select(t -> binomial(n, t) mod (n+t) = 0, [$0..n]))
end proc:
map(f, [$1..100]); # Robert Israel, Feb 27 2024
MATHEMATICA
A051556[n_] := Count[Divisible[Binomial[n, Range[0, n]], Range[n, 2*n]], True];
Array[A051556, 100] (* Paolo Xausa, Feb 29 2024 *)
PROG
(PARI) a(n) = sum(k=0, n, (binomial(n, k) % (n+k)) == 0); \\ Michel Marcus, May 18 2014
CROSSREFS
Cf. A051574 (similar definition).
Sequence in context: A286135 A375010 A142475 * A330166 A081602 A077267
KEYWORD
nonn
AUTHOR
STATUS
approved