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A308154
G.f.: x * Product_{j>=1, k>=1} (1 + a(j)*x^(j*k)).
1
1, 1, 2, 5, 11, 26, 64, 159, 397, 1042, 2701, 7249, 19341, 52927, 143615, 399359, 1099846, 3087498, 8616361, 24386458, 68617936, 195678409, 554862501, 1590363317, 4539073167, 13071768304, 37496646028, 108449257539, 312439316258, 906653694239, 2622887257356
OFFSET
1,3
MAPLE
A:= proc(n) option remember; series(x*`if`(n=1, 1, mul(mul(
1+a(j)*x^(j*k), k=1..(n-1)/j), j=1..n-1)), x, n+1)
end:
a:= n-> coeff(A(n), x, n):
seq(a(n), n=1..35); # Alois P. Heinz, May 14 2019
MATHEMATICA
a[n_] := a[n] = SeriesCoefficient[x Product[Product[(1 + a[j] x^(j k)), {k, 1, n - 1}], {j, 1, n - 1}], {x, 0, n}]; Table[a[n], {n, 1, 32}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 14 2019
STATUS
approved