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A115970 Expansion of 1/(4*sqrt(1-4x)-3). 7
1, 8, 72, 656, 5992, 54768, 500688, 4577568, 41851560, 382641200, 3498428272, 31985610720, 292439802256, 2673735097184, 24445577182368, 223502416896576, 2043450657688872, 18682977401318064, 170815793235313968 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The g.f. is A(x)^2/(2*A(x)-A(x)^2) where A(x) is the g.f. of A076035.

The Hankel transform of this sequence is 8^n = [1, 8, 64, 512, 4096, ...] ; The Hankel transform of the aerated sequence with g.f. 1/(1-8*x^2*c(x^2)) is also 8^n . - Philippe Deléham, Feb 13 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

G.f.: 1/(1-8*x*c(x)), where c(x) is the g.f. of A000108; a(n) = Sum_{k, 0<=k<=n} A106566(n, k)*8^k.

a(n)=(64*a(n-1)-8*A000108(n-1))/7 . a(n) = Sum_[k, 0<=k<=n} A039599(n,k)*7^k . a(n) = Sum_{k, 0<=k<=n} A106566(n,k)*8^k . - Philippe Deléham, Feb 13 2007

Recurrence: 7*n*a(n) = 2*(46*n-21)*a(n-1) - 128*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 3*2^(6*n+1)/7^(n+1). - Vaclav Kotesovec, Oct 19 2012

MATHEMATICA

CoefficientList[Series[1/(4*Sqrt[1-4*x]-3), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

CROSSREFS

Sequence in context: A055275 A155198 A147840 * A078995 A264913 A082414

Adjacent sequences:  A115967 A115968 A115969 * A115971 A115972 A115973

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 03 2006

STATUS

approved

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Last modified February 19 10:31 EST 2018. Contains 299330 sequences. (Running on oeis4.)