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A371364
Expansion of (1/x) * Series_Reversion( x * (1-4*x)^2 / (1-3*x) ).
4
1, 5, 49, 597, 8129, 118469, 1807665, 28512213, 461141761, 7606159365, 127454706609, 2163636679125, 37130370808257, 643099703566277, 11227141735655345, 197356077159062613, 3490230884900117505, 62054912214781757957, 1108568475427756051761
OFFSET
0,2
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..n} 3^(n-k) * binomial(2*n+k+1,k) * binomial(2*n,n-k).
D-finite with recurrence (n+1)*(2*n+1)*a(n) +3*(-6*n^2-9*n+2)*a(n-1) -27*(7*n-9)*(2*n-3)*a(n-2) -243*(n-2)*(2*n-5)*a(n-3)=0. - R. J. Mathar, Apr 22 2024
MAPLE
A371364 := proc(n)
add(3^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k), k=0..n) ;
%/(n+1) ;
end proc:
seq(A371364(n), n=0..60) ; # R. J. Mathar, Apr 22 2024
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-4*x)^2/(1-3*x))/x)
(PARI) a(n) = sum(k=0, n, 3^(n-k)*binomial(2*n+k+1, k)*binomial(2*n, n-k))/(n+1);
CROSSREFS
Sequence in context: A081474 A370097 A274671 * A112241 A216483 A243945
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 19 2024
STATUS
approved