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A212545
Number of partitions of n containing at least one part m-5 if m is the largest part.
2
0, 0, 1, 1, 3, 4, 8, 11, 19, 25, 39, 52, 75, 98, 137, 175, 236, 300, 393, 493, 635, 787, 997, 1227, 1531, 1869, 2309, 2796, 3420, 4119, 4994, 5979, 7201, 8574, 10260, 12164, 14470, 17082, 20225, 23778, 28025, 32838, 38542, 45011, 52642, 61286, 71434, 82937
OFFSET
5,5
LINKS
FORMULA
G.f.: Sum_{i>0} x^(2*i+5) / Product_{j=1..5+i} (1-x^j).
EXAMPLE
a(7) = 1: [6,1].
a(8) = 1: [6,1,1].
a(9) = 3: [6,1,1,1], [6,2,1], [7,2].
a(10) = 4: [6,1,1,1,1], [6,2,1,1], [6,3,1], [7,2,1].
a(11) = 8: [6,1,1,1,1,1], [6,2,1,1,1], [6,2,2,1], [6,3,1,1], [6,4,1], [7,2,1,1], [7,2,2], [8,3].
MAPLE
b:= proc(n, i) option remember;
`if`(n=0 or i=1, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i)))
end:
a:= n-> add(b(n-2*m-5, min(n-2*m-5, m+5)), m=1..(n-5)/2):
seq(a(n), n=5..60);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i == 1, 1, b[n, i - 1] + If[i > n, 0, b[n - i, i]]];
a[n_] := Sum[b[n - 2 m - 5, Min[n - 2 m - 5, m + 5]], {m, 1, (n - 5)/2}];
a /@ Range[5, 60] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A212551.
Sequence in context: A288566 A084421 A271723 * A357878 A358910 A212546
KEYWORD
nonn
AUTHOR
Alois P. Heinz, May 20 2012
STATUS
approved