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 A182803 Number of 8-core partitions of n. 3
 1, 1, 2, 3, 5, 7, 11, 15, 14, 22, 26, 32, 37, 45, 47, 56, 75, 77, 89, 102, 111, 124, 142, 147, 167, 182, 196, 210, 242, 249, 288, 322, 299, 349, 382, 393, 423, 467, 453, 499, 570, 563, 602, 669, 649, 716, 772, 754, 843, 907, 884 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA G.f.: Product_{i>=1} (1-x^(8*i))^8/(1-x^i). Euler transform of period 8 sequence [1,1,1,1,1,1,1,-7, .. ]. MAPLE 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, 8), n=0..50); MATHEMATICA A[n_, t_] := A[n, t] = 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]; Table[A[n, 8], {n, 0, 50}] (* Jean-François Alcover, May 21 2018, translated form Maple *) CROSSREFS 8th column of A175595. Sequence in context: A184642 A094252 A209038 * A106532 A240556 A090693 Adjacent sequences:  A182800 A182801 A182802 * A182804 A182805 A182806 KEYWORD nonn AUTHOR Alois P. Heinz, Dec 03 2010 STATUS approved

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Last modified August 19 07:51 EDT 2018. Contains 313857 sequences. (Running on oeis4.)