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 A369506 Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^2)^2 ). 0

%I #8 Jan 25 2024 07:50:08

%S 1,6,53,548,6192,74074,922142,11822082,155024190,2069570934,

%T 28033435791,384329462490,5322745393480,74357950874850,

%U 1046564375245893,14826433687124098,211251475010201934,3025331234242178508,43523061969049245589,628692982662691174722

%N Expansion of (1/x) * Series_Reversion( x / ((1+x)^3+x^2)^2 ).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+2,k) * binomial(6*n-3*k+6,n-2*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3+x^2)^2)/x)

%o (PARI) a(n) = sum(k=0, n\2, binomial(2*n+2, k)*binomial(6*n-3*k+6, n-2*k))/(n+1);

%Y Cf. A143927, A369503.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 25 2024

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Last modified August 11 03:32 EDT 2024. Contains 375059 sequences. (Running on oeis4.)