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A167479 Convolution of the Catalan numbers A000108(n) and (-2)^n. 1
1, -1, 4, -3, 20, 2, 128, 173, 1084, 2694, 11408, 35970, 136072, 470756, 1732928, 6228989, 22899692, 83845406, 309947888, 1147367414, 4269385592, 15927495836, 59627571968, 223804469714, 842295207896, 3177355985660, 12012641100832 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A079935.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

S. B. Ekhad, M. Yang, Proofs of Linear Recurrences of Coefficients of Certain Algebraic Formal Power Series Conjectured in the On-Line Encyclopedia Of Integer Sequences, (2017)

FORMULA

G.f.: c(x)/(1+2x), c(x) the g.f. of A000108.

a(n) = Sum_{k=0..n} (-2)^(n-k)*A000108(k).

Conjecture: (n+1)*a(n) + 2*(2-n)*a(n-1) + 4*(1-2*n)*a(n-2)=0. - R. J. Mathar, Nov 16 2011

a(n) ~ 2^(2*n + 1) / (3 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Mar 08 2018

MATHEMATICA

CoefficientList[Series[(1 - Sqrt[1 - 4*t])/(2*t*(1 + 2*t)), {t, 0, 50}], t] (* G. C. Greubel, Jun 13 2016 *)

CROSSREFS

Cf. A000108, A079935.

Sequence in context: A241358 A178417 A178628 * A278424 A278662 A220861

Adjacent sequences:  A167476 A167477 A167478 * A167480 A167481 A167482

KEYWORD

easy,sign

AUTHOR

Paul Barry, Nov 04 2009

STATUS

approved

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Last modified October 28 11:10 EDT 2020. Contains 338054 sequences. (Running on oeis4.)