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A307063
Expansion of 1/(2 - Product_{k>=1} (1 + k*x^k)).
5
1, 1, 3, 10, 28, 85, 252, 745, 2202, 6530, 19326, 57194, 169341, 501242, 1483816, 4392531, 13002772, 38491212, 113943278, 337298400, 998482338, 2955742400, 8749688247, 25901125616, 76673399424, 226971213462, 671887935923, 1988945626648, 5887744768722, 17429103155892, 51594226501776
OFFSET
0,3
COMMENTS
Invert transform of A022629.
a(n) is the number of compositions of n where there are A022629(k) sorts of part k. - Joerg Arndt, Jan 24 2024
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} A022629(k)*a(n-k).
MATHEMATICA
nmax = 30; CoefficientList[Series[1/(2 - Product[(1 + k x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
PROG
(Magma)
m:=80;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( 1/(2 - (&*[(1+j*x^j): j in [1..m+2]])) ));
(SageMath)
m=80;
def f(x): return 1/( 2 - product(1+j*x^j for j in range(1, m+3)) )
def A307063_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).list()
A307063_list(m) # G. C. Greubel, Jan 24 2024
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 21 2019
STATUS
approved