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A015743 Number of 8's in all the partitions of n into distinct parts. 2
0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 13, 15, 18, 22, 27, 31, 37, 44, 51, 61, 71, 82, 95, 111, 128, 148, 171, 195, 225, 258, 295, 337, 384, 437, 497, 565, 639, 724, 818, 923, 1042, 1173, 1319, 1483, 1665 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

LINKS

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 2000 terms from Robert Price)

FORMULA

G.f.: x^8*Product_{j>=1} (1+x^j)/(1+x^8). - Emeric Deutsch, Apr 17 2006

EXAMPLE

a(11)=2 because in the 12 (=A000009(11)) partitions of 11 into distinct parts, namely [11], [10,1], [9,2], [8,3], [8,2,1], [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2] and [5,3,2,1], altogether we have two parts equal to 8.

MAPLE

g:=x^8*product(1+x^j, j=1..60)/(1+x^8): gser:=series(g, x=0, 57): seq(coeff(gser, x, n), n=1..54); # Emeric Deutsch, Apr 17 2006

MATHEMATICA

Table[Count[Flatten@Select[IntegerPartitions[n], DeleteDuplicates[#] == # &], 8], {n, 54}] (* Robert Price, Jun 13 2020 *)

CROSSREFS

Sequence in context: A342499 A325096 A261771 * A015755 A096443 A126442

Adjacent sequences:  A015740 A015741 A015742 * A015744 A015745 A015746

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 12 07:28 EDT 2021. Contains 343821 sequences. (Running on oeis4.)