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A307059 Expansion of 1/(2 - Product_{k>=1} (1 - x^k)). 1
1, -1, 0, 1, -1, 1, -1, 1, 0, -2, 4, -4, 1, 3, -5, 4, -3, 3, -1, -6, 13, -12, 2, 9, -13, 10, -6, 6, -4, -9, 28, -30, 5, 25, -28, 5, 9, 7, -27, 11, 32, -47, 2, 51, -27, -74, 128, -34, -131, 183, -78, -15, -37, 97, 89, -480, 649, -242, -498, 904, -663, 223, -140, 169, 488, -1818 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

Invert transform of A010815.

Alternating row sums of Riordan triangle (1, -(Product_{j>=1} - 1), See A341418(n, m) without column {1, repeat(0)} for m = 0 and n >= 0. - Wolfdieter Lang, Feb 17 2021

LINKS

Table of n, a(n) for n=0..65.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} A010815(k)*a(n-k).

MATHEMATICA

nmax = 65; CoefficientList[Series[1/(2 - Product[(1 - x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

CROSSREFS

Cf. A010815, A055887, A299105, A341418.

Sequence in context: A295633 A159778 A243278 * A328412 A079536 A058923

Adjacent sequences:  A307056 A307057 A307058 * A307060 A307061 A307062

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Mar 21 2019

STATUS

approved

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Last modified May 13 05:02 EDT 2021. Contains 343836 sequences. (Running on oeis4.)