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A317536 Expansion of 1/(1 + 1/(1 - x) - Product_{k>=1} (1 + x^k)). 3
1, 0, 0, 1, 1, 2, 4, 6, 10, 18, 30, 50, 86, 145, 245, 417, 705, 1193, 2024, 3427, 5804, 9836, 16660, 28220, 47811, 80991, 137197, 232423, 393729, 666982, 1129898, 1914078, 3242495, 5492898, 9305130, 15763154, 26703273, 45236138, 76631348, 129815818, 219911870, 372537244, 631089250 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Invert transform of A111133.

LINKS

Table of n, a(n) for n=0..42.

N. J. A. Sloane, Transforms

FORMULA

G.f.: 1/(1 - Sum_{k>=1} A111133(k)*x^k).

MAPLE

seq(coeff(series(1/(1+1/(1-x)-mul(1+x^k, k=1..n)), x, n+1), x, n), n=0..50); # Muniru A Asiru, Jul 30 2018

MATHEMATICA

nmax = 42; CoefficientList[Series[1/(1 + 1/(1 - x) - Product[(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

nmax = 42; CoefficientList[Series[1/(1 - Sum[(PartitionsQ[k] - 1) x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[(PartitionsQ[k] - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]

CROSSREFS

Cf. A000009, A050342, A089259, A111133, A270995, A279785, A299106, A304969, A305651, A317535.

Sequence in context: A142584 A098197 A175941 * A203175 A102477 A232582

Adjacent sequences:  A317533 A317534 A317535 * A317537 A317538 A317539

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 30 2018

STATUS

approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)