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Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+5) / (3*k+5)! ).
2

%I #11 Sep 23 2023 07:27:18

%S 1,0,0,0,0,1,0,0,1,0,252,1,0,2574,1,756756,21606,1,33081048,174420,

%T 11732745025,1052328186,1397640,1484192245537,30223445274,

%U 623360754309330,126750660276241,835509726090,182333017453575330,9309138073555321

%N Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+5) / (3*k+5)! ).

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/3)} binomial(n,3*k+5) * a(n-3*k-5).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+5)/(3*k+5)!))))

%Y Cf. A245790, A365915, A365917.

%Y Cf. A365897.

%K nonn,easy

%O 0,11

%A _Seiichi Manyama_, Sep 23 2023