A367757 - OEIS

%I #6 Nov 29 2023 11:47:52

%S 1,1,3,13,73,501,3337,27637,254409,2557369,27603631,313768731,

%T 3905502745,51573777841,718307494269,10507900625251,161239887204721,

%U 2608009648536417,43989477103304155,772109936171046001,14085074476090366761,266890182641557777093

%N E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3 + x^4) * A(x^5/120)).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/5)) * a(n-1-k) / (120^floor(k/5) * floor(k/5)! * (n-1-k)!).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=0, i-1, (j+1)*v[j\5+1]*v[i-j]/(120^(j\5)*(j\5)!*(i-1-j)!))); v;

%Y Cf. A367754, A367755, A367756.

%Y Cf. A143569.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 29 2023