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A279786
Twice-partitioned numbers where the first partition is strict and the latter partitions are constant.
18
1, 1, 2, 4, 5, 9, 16, 22, 28, 49, 69, 94, 138, 187, 257, 374, 479, 639, 886, 1146, 1577, 2103, 2676, 3534, 4620, 5910, 7542, 9816, 12650, 15986, 20538, 25740, 32632, 41442, 51383, 64771, 81281, 100729, 125041, 155557, 192641, 236810, 293593, 359880, 441276
OFFSET
0,3
FORMULA
G.f.: exp(Sum_{k>=1} Sum_{j>=1} (-1)^(k+1)*d(j)^k*x^(j*k)/k), where d(j) is the number of the divisors of j (A000005). - Ilya Gutkovskiy, Jul 17 2018
EXAMPLE
The a(5)=9 twice-partitions are:
((5)), ((4)(1)), ((3)(2)), ((3)(11)), ((22)(1)),
((111)(2)), ((111)(11)), ((1111)(1)), ((11111)).
MAPLE
b:= proc(n, i) option remember;
`if`(n>i*(i+1)/2, 0, `if`(n=0, 1, b(n, i-1)+
`if`(i>n, 0, numtheory[tau](i)*b(n-i, i-1))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..70); # Alois P. Heinz, Dec 20 2016
MATHEMATICA
nn=20; CoefficientList[Series[Product[(1+DivisorSigma[0, n]x^n), {n, nn}], {x, 0, nn}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 18 2016
STATUS
approved