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Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+1) / (3*k+1) ).
2

%I #9 Sep 24 2023 09:16:16

%S 1,1,2,6,30,180,1260,10800,104760,1130760,13776480,184044960,

%T 2670220080,42222280320,718144004160,13061603808000,254036916144000,

%U 5247117638294400,114652672773408000,2647321293055507200,64330669872690566400,1640738743703289331200

%N Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+1) / (3*k+1) ).

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+1)/(3*k+1)))))

%Y Cf. A296676, A365976, A365977.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Sep 23 2023