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A051951 Second differences of tau(n). 1
0, -1, 1, -2, 3, -4, 4, -3, 2, -3, 6, -8, 6, -2, 1, -4, 7, -8, 8, -6, 2, -2, 8, -11, 6, -1, 2, -6, 10, -12, 10, -6, 2, 0, 5, -12, 9, -2, 4, -10, 12, -12, 10, -4, -2, 0, 10, -15, 10, -5, 4, -6, 10, -10, 8, -8, 4, -2, 12, -20, 12, 0, -1, -4, 7, -10, 10, -6, 6, -10, 16, -20, 12, 0, -2, -2, 6, -10, 14, -13, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(0) = 0 assuming tau(0) = 0. - Michael Somos, Mar 05 2014

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

G.f.: -1/x + (1 - x)^2*Sum_{k>=1} x^(k-2)/(1 - x^k). - Ilya Gutkovskiy, Jan 29 2017

EXAMPLE

G.f. = - x + x^2 - 2*x^3 + 3*x^4 - 4*x^5 + 4*x^6 - 3*x^7 + 2*x^8 - 3*x^9 + ...

MAPLE

Taus:= map(numtheory:-tau, [$0..100]):

Taus[3..-1] - 2*Taus[2..-2] + Taus[1..-3]; # Robert Israel, Dec 07 2015

MATHEMATICA

Join[{0}, Differences[DivisorSigma[0, Range[90]], 2]] (* Harvey P. Dale, Jan 10 2014 *)

a[ n_] := SeriesCoefficient[ (QHypergeometricPFQ[ {x, x}, {x^2, x^2}, x, x^2] - 1) / x, {x, 0, n}]; (* Michael Somos, Mar 05 2014 *)

CROSSREFS

Cf. A000005, A051950.

Sequence in context: A167831 A090281 A316823 * A262857 A107898 A128863

Adjacent sequences:  A051948 A051949 A051950 * A051952 A051953 A051954

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Dec 17 1999

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)