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E.g.f. satisfies A(x) = exp( x*A(x)^4/(1 - x*A(x)^2) ).
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%I #13 Mar 14 2023 03:41:54

%S 1,1,11,241,8105,370061,21403675,1500521485,123685912817,

%T 11724012791929,1256517775425131,150254377493878505,

%U 19833528195709809817,2864566162751107839493,449364739762263286489403,76084967168410028438252101,13829896583435315152843525985

%N E.g.f. satisfies A(x) = exp( x*A(x)^4/(1 - x*A(x)^2) ).

%H Winston de Greef, <a href="/A361143/b361143.txt">Table of n, a(n) for n = 0..315</a>

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

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

%Y Cf. A000262, A361142.

%Y Cf. A212722, A361065, A361093.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 02 2023