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A369023 Expansion of (1/x) * Series_Reversion( x * (1-2*x)^3 / (1-x) ). 4
1, 5, 43, 451, 5253, 65297, 848503, 11387047, 156602761, 2195519965, 31261365155, 450840279787, 6571775541069, 96669928040745, 1433170971310191, 21392403565317839, 321228841377255953, 4849129915768191413, 73545708989920501147, 1120169585882592246419 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(3*n+1,n-k).
D-finite with recurrence 27*(3*n+2)*(3*n+1)*(n+1)*a(n) +9*(-689*n^3 +263*n^2 -132*n +16)*a(n-1) +6*(6039*n^3 -20979*n^2 +23222*n -8050)*a(n-2) +(43*n^3 -5790*n^2 +25097*n -27570)*a(n-3) -15*(3*n-10)*(3*n-8)*(n-3)*a(n-4)=0. - R. J. Mathar, Jan 25 2024
MAPLE
A369023 := proc(n)
add(binomial(3*n+k+2, k) * binomial(3*n+1, n-k), k=0..n) ;
%/(n+1) ;
end proc;
seq(A369023(n), n=0..70) ; % R. J. Mathar, Jan 25 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^3/(1-x))/x)
(PARI) a(n, s=1, t=3, u=-1) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
CROSSREFS
Sequence in context: A112115 A350117 A239265 * A274666 A301976 A083070
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 12 2024
STATUS
approved

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)