A015742 Number of 7's in all the partitions of n into distinct parts.

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

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