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A098483 Expansion of 1/sqrt((1-x)^2-8x^4). 3
1, 1, 1, 1, 5, 13, 25, 41, 85, 205, 473, 985, 2021, 4365, 9785, 21673, 46965, 101581, 222745, 492665, 1087237, 2388749, 5251065, 11587529, 25633045, 56697933, 125345113, 277283353, 614212133, 1361824525, 3020426681, 6700678377 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

1/sqrt((1-x)^2-4rx^4) expands to sum{k=0..floor(n/2), binomial(n-2k,k)binomial(n-3k,k)r^k}

LINKS

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

FORMULA

a(n)=sum{k=0..floor(n/2), binomial(n-2k, k)binomial(n-3k, k)2^k}.

D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) + 8*(n-2)*a(n-4). - Vaclav Kotesovec, Jun 23 2014

a(n) ~ (1+sqrt(1+8*sqrt(2)))^n / (sqrt(33+10*sqrt(2)-sqrt(265+596*sqrt(2))) * sqrt(Pi*n) * 2^(n-3/2)). - Vaclav Kotesovec, Jun 23 2014

MATHEMATICA

CoefficientList[Series[1/Sqrt[(1-x)^2-8*x^4], {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 23 2014 *)

PROG

(PARI) a(n) = sum(k=0, n\2, binomial(n-2*k, k)*binomial(n-3*k, k)*2^k) \\ Michel Marcus, Jul 24 2013

CROSSREFS

Cf. A098480, A098482, A098484.

Sequence in context: A301671 A268525 A146590 * A147205 A146875 A241233

Adjacent sequences: A098480 A098481 A098482 * A098484 A098485 A098486

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 10 2004

STATUS

approved

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Last modified February 3 07:57 EST 2023. Contains 360024 sequences. (Running on oeis4.)