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A222735
Total sum of parts of multiplicity 7 in all partitions of n.
2
1, 0, 1, 1, 2, 2, 4, 6, 9, 10, 16, 20, 29, 36, 53, 66, 91, 112, 152, 190, 251, 315, 409, 510, 655, 809, 1029, 1271, 1602, 1967, 2457, 3009, 3729, 4543, 5595, 6801, 8321, 10069, 12258, 14783, 17906, 21511, 25947, 31073, 37315, 44542, 53285, 63415, 75587, 89687
OFFSET
7,5
LINKS
FORMULA
G.f.: (x^7/(1-x^7)^2-x^8/(1-x^8)^2)/Product_{i>=1}(1-x^i).
a(n) ~ 15 * sqrt(3) * exp(Pi*sqrt(2*n/3)) / (6272 * Pi^2). - Vaclav Kotesovec, May 29 2018
MAPLE
b:= proc(n, p) option remember; `if`(n=0, [1, 0], `if`(p<1, [0, 0],
add((l->`if`(m=7, l+[0, l[1]*p], l))(b(n-p*m, p-1)), m=0..n/p)))
end:
a:= n-> b(n, n)[2]:
seq(a(n), n=7..60);
MATHEMATICA
b[n_, p_] := b[n, p] = If[n == 0 && p == 0, {1, 0}, If[p == 0, Array[0&, n+2], Sum[Function[l, ReplacePart[l, m+2 -> p*l[[1]] + l[[m+2]]]][Join[b[n-p*m, p-1], Array[0&, p*m]]], {m, 0, n/p}]]]; a[n_] := b[n, n][[9]]; Table[a[n], {n, 7, 60}] (* Jean-François Alcover, Jan 24 2014, after Alois P. Heinz *)
CROSSREFS
Column k=7 of A222730.
Sequence in context: A231187 A055529 A337723 * A299408 A338937 A319381
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Mar 03 2013
STATUS
approved