

A216221


Triangular array read by rows. T(n,k) is the number of partitions of n (using 1 type of part 1, 2 types of part 2, ..., i types of part i, ...) that have exactly k distinct parts.


0



1, 3, 4, 2, 7, 6, 6, 17, 1, 12, 29, 7, 8, 55, 23, 15, 84, 58, 3, 13, 122, 134, 13, 18, 181, 249, 52, 12, 240, 464, 140, 3, 28, 321, 765, 348, 17, 14, 407, 1249, 746, 69, 24, 546, 1875, 1501, 220, 1, 24, 628, 2835, 2793, 586, 13, 31, 828, 4024, 4927, 1431, 56, 18, 940, 5707, 8331, 3123, 215, 39, 1211, 7741, 13520, 6436, 650, 4
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OFFSET

1,2


COMMENTS



LINKS



FORMULA

O.g.f.: Product_{i>=1} (1 + y*x^i/(1x^i))^i.


EXAMPLE

1,
3,
4, 2,
7, 6,
6, 17, 1,
12, 29, 7,
8, 55, 23,
15, 84, 58, 3,
13, 122, 134, 13,
18, 181, 249, 52,
12, 240, 464, 140, 3,
28, 321, 765, 348, 17,
14, 407, 1249, 746, 69,
24, 546, 1875, 1501, 220, 1
24, 628, 2835, 2793, 586, 13
T(4,2) = 6 because we have: 3+1, 3'+1, 3''+1, 2+2', 2+1+1, 2'+1+1.


MATHEMATICA

nn=15; f[list_]:=Select[list, #>0&]; Map[f, Drop[CoefficientList[Series[ Product[(1+y x^i/(1x^i))^i, {i, 1, nn}], {x, 0, nn}], {x, y}], 1]]//Grid


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



