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A098405 Expansion of ((1-sqrt(1-8*x))/((1-x)*(4*x*sqrt(1-8*x))). 1
1, 7, 47, 327, 2343, 17127, 126951, 950631, 7173991, 54471527, 415652711, 3184708455, 24485137255, 188802730855, 1459525454695, 11307626564455, 87775235181415, 682523302202215, 5315297718995815, 41450938169985895, 323653082644384615, 2529960757626047335 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Partial sums of A069720.

LINKS

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

FORMULA

a(n) = sum{k=0..n, Binomial(2k+1, k)*2^k}

D-finite with recurrence: (n+1)*a(n) = (9*n+5)*a(n-1) - 4*(2*n+1)*a(n-2). - Vaclav Kotesovec, Oct 15 2012

a(n) ~ 2^(3*n+4)/(7*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012

MATHEMATICA

Table[SeriesCoefficient[(1-Sqrt[1-8*x])/((1-x)*(4*x*Sqrt[1-8*x])), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 15 2012 *)

Accumulate[Table[2^(n-1) Binomial[2n-1, n], {n, 20}]] (* Harvey P. Dale, Jan 20 2013 *)

PROG

(PARI) x='x+O('x^66); Vec((1-sqrt(1-8*x))/((1-x)*(4*x*sqrt(1-8*x)))) \\ Joerg Arndt, May 11 2013

CROSSREFS

Sequence in context: A126528 A214992 A241364 * A104092 A024187 A001711

Adjacent sequences: A098402 A098403 A098404 * A098406 A098407 A098408

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 06 2004

STATUS

approved

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Last modified January 29 21:02 EST 2023. Contains 359931 sequences. (Running on oeis4.)