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A162478 Expansion of 1/sqrt(1-4x/(1-x)^4). 2
1, 2, 14, 88, 566, 3722, 24856, 167868, 1143462, 7841434, 54065574, 374437404, 2602879712, 18150990238, 126918338116, 889551010728, 6247598686710, 43958881741086, 309801915943318, 2186512103767096, 15452093394793006 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums are A162479.

LINKS

Robert Israel, Table of n, a(n) for n = 0..1163

FORMULA

G.f.: 1/(1-2x/((1-x)^4-x/(1-x/((1-x)^4-x/(1-... (continued fraction);

a(n)=sum{k=0..n, C(n+3k-1,n-k)*A000984(k)}.

D-finite with recurrence: n*a(n) +(7-9n)*a(n-1) +2*(7n-17)*a(n-2) +10*(3-n)*a(n-3) +5*(n-4)*a(n-4) +(5-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011

Recurrence confirmed using the differential equation (6*x+2)*g+(x^5-5*x^4+10*x^3-14*x^2+9*x-1)*g'=0 satisfied by the G.f. - Robert Israel, Dec 27 2017

MAPLE

f:= gfun:-rectoproc({n*a(n) +(7-9*n)*a(n-1) +2*(7*n-17)*a(n-2) +10*(3-n)*a(n-3) +5*(n-4)*a(n-4) +(5-n)*a(n-5), a(0)=1, a(1)=2, a(2)=14, a(3)=88, a(4)=566}, a(n), remember):

map(f, [$0..50]); # Robert Israel, Dec 27 2017

MATHEMATICA

CoefficientList[Series[1/Sqrt[1-(4x)/(1-x)^4], {x, 0, 20}], x] (* Harvey P. Dale, Aug 02 2016 *)

CROSSREFS

Sequence in context: A037563 A005610 A065355 * A189392 A235374 A065892

Adjacent sequences:  A162475 A162476 A162477 * A162479 A162480 A162481

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 04 2009

STATUS

approved

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Last modified July 5 04:30 EDT 2020. Contains 335459 sequences. (Running on oeis4.)