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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 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 October 21 06:25 EDT 2019. Contains 328292 sequences. (Running on oeis4.)