A367754 E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x^2/2)).

1, 1, 3, 10, 49, 276, 1921, 14533, 127905, 1214524, 12923641, 146976501, 1828895113, 24160939960, 343798990809, 5162735472196, 82578544952641, 1387325644153368, 24621686929968625, 457066782857330929, 8906813110169504841, 180902690843146001416

Offset: 0

Author

Seiichi Manyama, Nov 29 2023

Keywords

• nonn

Crossrefs

Cf. A367755, A367756, A367757.

Cf. A143566.

Programs

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;

Formula

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)!).