The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307076 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A307076

Expansion of 1/(1 - Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).
(history; published version)

#6 by Bruno Berselli at Sat Mar 23 12:39:01 EDT 2019

STATUS

reviewed

approved

#5 by Bruno Berselli at Sat Mar 23 12:38:56 EDT 2019

STATUS

proposed

reviewed

#4 by Ilya Gutkovskiy at Fri Mar 22 12:54:42 EDT 2019

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Fri Mar 22 12:46:42 EDT 2019

NAME

allocated for Ilya GutkovskiyExpansion of 1/(1 - Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).

DATA

1, 1, 0, -2, -2, 0, 4, 4, -2, -10, -6, 10, 22, 4, -34, -46, 16, 102, 86, -100, -272, -126, 370, 650, 60, -1138, -1384, 526, 3142, 2532, -2936, -7952, -3440, 10802, 18426, 596, -33344, -38418, 18716, 91934, 68400, -93402, -230962, -86236, 330144, 528880, -17298, -996040

OFFSET

0,4

COMMENTS

Invert transform of A008836.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} A008836(k)*a(n-k).

MATHEMATICA

nmax = 47; CoefficientList[Series[1/(1 - Sum[LiouvilleLambda[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

a[0] = 1; a[n_] := a[n] = Sum[LiouvilleLambda[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 47}]

CROSSREFS

Cf. A008836, A118206, A118207, A300663.

KEYWORD

allocated

sign

AUTHOR

Ilya Gutkovskiy, Mar 22 2019

STATUS

approved

editing

#2 by Ilya Gutkovskiy at Fri Mar 22 12:46:42 EDT 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved