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A320790
Number of multisets of exactly five partitions of positive integers into distinct parts with total sum of parts equal to n.
2
1, 1, 3, 5, 11, 19, 36, 60, 107, 176, 296, 475, 770, 1211, 1906, 2939, 4518, 6842, 10313, 15363, 22770, 33424, 48802, 70688, 101854, 145755, 207528, 293704, 413691, 579571, 808328, 1121923, 1550645, 2133751, 2924579, 3992307, 5429751, 7357195, 9934357
OFFSET
5,3
LINKS
FORMULA
a(n) = [x^n y^5] Product_{j>=1} 1/(1-y*x^j)^A000009(j).
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(add(`if`(d::odd,
d, 0), d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
add(b(n-i*j, i-1)*x^j*binomial(g(i)+j-1, j), j=0..n/i))), x, 6)
end:
a:= n-> coeff(b(n$2), x, 5):
seq(a(n), n=5..60);
MATHEMATICA
g[n_] := g[n] = If[n == 0, 1, Sum[Sum[If[OddQ[d], d, 0], {d, Divisors[j]}]* g[n - j], {j, 1, n}]/n];
b[n_, i_] := b[n, i] = Series[If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]*x^j*Binomial[g[i] + j - 1, j], {j, 0, n/i}]]], {x, 0, 6}];
a[n_] := SeriesCoefficient[b[n, n], {x, 0, 5}];
a /@ Range[5, 60] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A285229.
Cf. A000009.
Sequence in context: A329178 A298348 A303005 * A175783 A078722 A320791
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 21 2018
STATUS
approved