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A239488 Expansion of 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3. 0
6, 30, 186, 1290, 9582, 74550, 599730, 4948050, 41638614, 356007630, 3083837802, 27006251610, 238704231102, 2126733078630, 19079571337314, 172209370246050, 1562686251141030, 14248144422407550, 130467052593799962 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = sum(i = 0..n+1, 2^i*binomial(n,n-i+1)*binomial(n+i-1,n-1))/n.
a(n) = T(2*n,n-1)/n where T(n,k) is triangle A116412.
D-finite with recurrence: (n+1)*a(n) +5*(-2*n+1)*a(n-1) +(n-2)*a(n-2)=0. a(n) = 2*A103210(n). - R. J. Mathar, May 23 2014
MAPLE
ogf := 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3;
series(ogf, x=0, 20): seq(coeff(%, x, n), n=0..19); # Peter Luschny, Mar 21 2014
PROG
(Maxima) a(n):=sum(2^i*binomial(n, n-i+1)*binomial(n+i-1, n-1), i, 0, n+1)/n;
CROSSREFS
Cf. A103210.
Sequence in context: A368524 A259276 A109501 * A147517 A294221 A005922
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Mar 20 2014
STATUS
approved

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Last modified May 26 16:43 EDT 2024. Contains 372840 sequences. (Running on oeis4.)