A367754 - OEIS

%I #8 Nov 29 2023 11:43:25

%S 1,1,3,10,49,276,1921,14533,127905,1214524,12923641,146976501,

%T 1828895113,24160939960,343798990809,5162735472196,82578544952641,

%U 1387325644153368,24621686929968625,457066782857330929,8906813110169504841,180902690843146001416

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

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..n-1} (k+1) * a(floor(k/2)) * a(n-1-k) / (2^floor(k/2) * floor(k/2)! * (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\2+1]*v[i-j]/(2^(j\2)*(j\2)!*(i-1-j)!))); v;

%Y Cf. A367755, A367756, A367757.

%Y Cf. A143566.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 29 2023