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A182805 Number of 10-core partitions of n. 2
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 32, 46, 57, 71, 85, 106, 121, 147, 165, 190, 242, 267, 302, 350, 400, 443, 511, 565, 638, 715, 774, 852, 964, 1038, 1135, 1253, 1372, 1482, 1650, 1785, 1878, 2098, 2234, 2411, 2625, 2819, 2963, 3249, 3393, 3600, 4004, 4181 (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^(10*i))^10/(1-x^i).

Euler transform of period 10 sequence [1,1,1,1,1,1,1,1,1,-9, .. ].

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, 10), n=0..50);

MATHEMATICA

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]];

Table[A[n, 10], {n, 0, 50}] (* Jean-Fran├žois Alcover, Dec 06 2020, after Alois P. Heinz *)

CROSSREFS

10th column of A175595.

Cf. A033687, A045831, A053723, A081622, A053724, A182803, A182804.

Sequence in context: A027343 A184644 A209039 * A309058 A218509 A026815

Adjacent sequences:  A182802 A182803 A182804 * A182806 A182807 A182808

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Dec 03 2010

STATUS

approved

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)