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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Emeric Deutsch, Apr 17 2006
STATUS
approved