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A015742 Number of 7's in all the partitions of n into distinct parts. 2
0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 10, 12, 14, 18, 22, 25, 30, 36, 42, 50, 58, 67, 79, 92, 106, 123, 142, 164, 189, 217, 248, 284, 325, 370, 421, 479, 543, 616, 698, 788, 890, 1005, 1131, 1273, 1432, 1606, 1802 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

FORMULA

G.f.: x^7*(Product_{j>=1} (1+x^j))/(1+x^7). - Emeric Deutsch, Apr 17 2006

a(n) ~ exp(Pi*sqrt(n/3)) / (8*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Oct 30 2015

EXAMPLE

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

MAPLE

g:=x^7*product(1+x^j, j=1..60)/(1+x^7): gser:=series(g, x=0, 57): seq(coeff(gser, x, n), n=1..54); # Emeric Deutsch, Apr 17 2006

MATHEMATICA

n7[n_]:=Count[Flatten[Select[IntegerPartitions[n], Max[Transpose[ Tally[#]][[2]]]==1&]], 7]; Table[n7[n], {n, 60}] (* Harvey P. Dale, Aug 30 2013 *)

nmax = 100; Rest[CoefficientList[Series[x^7/(1+x^7) * Product[1+x^k, {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Oct 30 2015 *)

CROSSREFS

Sequence in context: A104648 A141271 A097793 * A015754 A207613 A321424

Adjacent sequences:  A015739 A015740 A015741 * A015743 A015744 A015745

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Emeric Deutsch, Apr 17 2006

STATUS

approved

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Last modified April 15 09:32 EDT 2021. Contains 342977 sequences. (Running on oeis4.)