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A320736
Number of partitions of n with five sorts of part 1 which are introduced in ascending order.
4
1, 1, 3, 7, 20, 63, 232, 944, 4158, 19236, 91794, 446311, 2194569, 10863768, 53995350, 269013587, 1342192961, 6702368648, 33486112079, 167353481065, 836536395240, 4181989400979, 20907870188551, 104533122311131, 522646929294281, 2613178606952285
OFFSET
0,3
LINKS
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
Stirling2(n, j), j=0..5), add(b(n-i*j, i-1), j=0..n/i))
end:
a:= n-> b(n$2):
seq(a(n), n=0..40);
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0 || i < 2, Sum[StirlingS2[n, j], {j, 0, 5}], Sum[b[n - i j, i - 1], {j, 0, n/i}]];
a[n_] := b[n, n];
a /@ Range[0, 40] (* Jean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
CROSSREFS
Column k=5 of A292745.
Sequence in context: A056783 A320735 A176697 * A320737 A320738 A320739
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2018
STATUS
approved