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Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x)^4 ).
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%I #16 Sep 20 2023 10:00:37

%S 1,8,96,1368,21440,356968,6197408,110947768,2033381760,37963483592,

%T 719495148768,13806129179928,267693334199616,5236670783633960,

%U 103227182363423008,2048451544990578552,40888361539777714944,820400146864231266184

%N Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1+x)^4 ).

%F a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(4*n+k+3,k) * binomial(4*(n+1),n-k).

%F Conjecture: g.f.: B^4, where B is the g.f. of A260332.

%o (PARI) a(n) = sum(k=0, n, binomial(4*n+k+3, k)*binomial(4*(n+1), n-k))/(n+1);

%Y Cf. A066357, A365754, A365846, A365848.

%Y Cf. A032349, A365622, A365843.

%Y Cf. A260332.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 20 2023