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A320733
Number of partitions of n with two sorts of part 1 which are introduced in ascending order.
3
1, 1, 3, 6, 13, 26, 54, 108, 219, 439, 882, 1766, 3539, 7081, 14172, 28351, 56716, 113443, 226908, 453833, 907698, 1815424, 3630893, 7261829, 14523725, 29047513, 58095121, 116190338, 232380810, 464761759, 929523710, 1859047619, 3718095507, 7436191301
OFFSET
0,3
LINKS
FORMULA
G.f.: ((1 - x)/(1 - 2*x)) * Product_{k>=2} 1/(1 - x^k). - Ilya Gutkovskiy, Dec 03 2019
MAPLE
b:= proc(n, i) option remember; `if`(n=0 or i<2, add(
Stirling2(n, j), j=0..2), 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, 2}], 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=2 of A292745.
Sequence in context: A081254 A125049 A267581 * A164991 A213255 A215985
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 20 2018
STATUS
approved