%I #17 Dec 06 2020 09:03:12
%S 1,1,2,3,5,7,11,15,22,30,32,46,57,71,85,106,121,147,165,190,242,267,
%T 302,350,400,443,511,565,638,715,774,852,964,1038,1135,1253,1372,1482,
%U 1650,1785,1878,2098,2234,2411,2625,2819,2963,3249,3393,3600,4004,4181
%N Number of 10-core partitions of n.
%H Alois P. Heinz, <a href="/A182805/b182805.txt">Table of n, a(n) for n = 0..10000</a>
%F G.f.: Product_{i>=1} (1-x^(10*i))^10/(1-x^i).
%F Euler transform of period 10 sequence [1,1,1,1,1,1,1,1,1,-9, .. ].
%p with(numtheory): A:= proc(n, t) option remember; local d, j; `if`(n=0, 1, add(add(`if`(t=0 or irem(d, t)=0, d-d*t, d), d=divisors(j)) *A(n-j, t), j=1..n)/n) end: seq(A(n,10), n=0..50);
%t A[n_, t_] := A[n, t] = Module[{d, j}, If[n == 0, 1, Sum[Sum[If[t == 0 || Mod[d, t] == 0, d - d t, d], {d, Divisors[j]}] A[n - j, t], {j, 1, n}]/n]];
%t Table[A[n, 10], {n, 0, 50}] (* _Jean-François Alcover_, Dec 06 2020, after _Alois P. Heinz_ *)
%Y 10th column of A175595.
%Y Cf. A033687, A045831, A053723, A081622, A053724, A182803, A182804.
%K nonn
%O 0,3
%A _Alois P. Heinz_, Dec 03 2010