A317535 Expansion of 1/(1 + 1/(1 - x) - Product_{k>=1} 1/(1 - x^k)).

1, 0, 1, 2, 5, 10, 23, 48, 106, 227, 494, 1065, 2310, 4991, 10808, 23376, 50593, 109455, 236858, 512479, 1108924, 2399418, 5191853, 11233929, 24307777, 52596430, 113806948, 246252376, 532834797, 1152933975, 2494689316, 5397944266, 11679933875, 25272740480, 54684508281, 118324934647

Offset: 0

Author

Ilya Gutkovskiy, Jul 30 2018

Keywords

• nonn

Comments

Invert transform of A000065.

Links

• Robert Israel, Table of n, a(n) for n = 0..2000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000041, A000065, A001970, A055887, A063834, A261049, A271619, A304966, A317536.

Programs

Maple

seq(coeff(series(1/(1+1/(1-x)-mul(1/(1-x^k),k=1..n)), x,n+1),x,n),n=0..40); # Muniru A Asiru, Jul 30 2018

Mathematica

nmax = 35; CoefficientList[Series[1/(1 + 1/(1 - x) - Product[1/(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 35; CoefficientList[Series[1/(1 - Sum[(PartitionsP[k] - 1) x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = Sum[(PartitionsP[k] - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 35}]

Formula

G.f.: 1/(1 - Sum_{k>=1} A000065(k)*x^k).