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A156195 a(2n+2)=6*a(2n+1), a(2n+1)=6*a(2n)-5^n*A000108(n), a(0)=1 . 6
1, 5, 30, 175, 1050, 6250, 37500, 224375, 1346250, 8068750, 48412500, 290343750, 1742062500, 10450312500, 62701875000, 376177734375, 2257066406250, 13541839843750, 81251039062500, 487496738281250, 2924980429687500, 17549718554687500, 105298311328125000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is 5^C(n+1,2). [From Philippe Deléham, Feb 05 2009]

LINKS

Table of n, a(n) for n=0..22.

P. Barry, A Note on a One-Parameter Family of Catalan-Like Numbers, JIS 12 (2009) 09.5.4

FORMULA

a(n)=sum{k=0..n, A120730(n,k)*5^k}.

G.f.: (sqrt(1-20*x^2)+10*x-1)/(10*x*(1-6x)). [From Philippe Deléham, Feb 05 2009]

Conjecture: (n+1)*a(n) +6*(-n-1)*a(n-1) +20*(-n+2)*a(n-2) +120*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 21 2016

MAPLE

A156195 := proc(n)

    option remember;

    local nh;

    if n= 0 then

        1;

    elif  type(n, 'even') then

        6*procname(n-1);

    else

        nh := floor(n/2) ;

        6*procname(n-1)-5^nh*A000108(nh) ;

    end if;

end proc: # R. J. Mathar, Jul 21 2016

MATHEMATICA

CoefficientList[Series[(Sqrt[1-20x^2]+10x-1)/(10x(1-6x)), {x, 0, 30}], x] (* Harvey P. Dale, Oct 21 2016 *)

CROSSREFS

Cf. A000108, A156058, A001405, A151281, A151162, A151254

Sequence in context: A229246 A276598 A057088 * A105481 A242157 A094167

Adjacent sequences:  A156192 A156193 A156194 * A156196 A156197 A156198

KEYWORD

nonn

AUTHOR

Philippe Deléham, Feb 05 2009

EXTENSIONS

Corrected and extended by Harvey P. Dale, Oct 21 2016

STATUS

approved

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Last modified February 25 06:31 EST 2018. Contains 299643 sequences. (Running on oeis4.)