|
|
A218573
|
|
Number of partitions p of n such that max(p)-min(p) = 10.
|
|
4
|
|
|
1, 1, 3, 3, 7, 8, 14, 18, 28, 35, 53, 67, 93, 119, 161, 201, 267, 332, 428, 531, 674, 824, 1034, 1258, 1552, 1877, 2294, 2749, 3332, 3970, 4762, 5645, 6723, 7916, 9367, 10974, 12894, 15036, 17571, 20381, 23696, 27370, 31652, 36416, 41926, 48029, 55071, 62860
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
12,3
|
|
LINKS
|
|
|
FORMULA
|
G.f.: Sum_{k>0} x^(2*k+10)/Product_{j=0..10} (1-x^(k+j)).
|
|
MATHEMATICA
|
terms = 48; offset = 12; max = terms + offset; s[k0_ /; k0 > 0] := Sum[x^(2*k + k0)/Product[ (1 - x^(k + j)), {j, 0, k0}], {k, 1, Ceiling[max/2]}] + O[x]^max // CoefficientList[#, x] &; Drop[s[10], offset] (* Jean-François Alcover, Sep 11 2017, after Alois P. Heinz *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|