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

%I #9 Sep 24 2023 09:16:27

%S 1,0,1,0,6,24,90,1008,7560,54432,712152,7620480,81130896,1266632640,

%T 17587441872,246734377344,4527397929600,77238618702336,

%U 1340945212763520,28407941067018240,574640938744314624,11868502219930137600,285787326567523173120

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+2)/(3*k+2)))))

%Y Cf. A226226, A365979.

%Y Cf. A365908.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 23 2023