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A317535 Expansion of 1/(1 + 1/(1 - x) - Product_{k>=1} 1/(1 - x^k)). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Invert transform of A000065.

LINKS

Table of n, a(n) for n=0..35.

N. J. A. Sloane, Transforms

FORMULA

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

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}]

CROSSREFS

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

Sequence in context: A284181 A291249 A260744 * A087640 A116953 A099516

Adjacent sequences:  A317532 A317533 A317534 * A317536 A317537 A317538

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 30 2018

STATUS

approved

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Last modified November 30 19:02 EST 2021. Contains 349424 sequences. (Running on oeis4.)