A367747 E.g.f. satisfies A(x) = exp(x * (1 + x) * A(x^2)).

1, 1, 3, 13, 73, 561, 4771, 49813, 562353, 7340833, 102829411, 1627648221, 27294311353, 502042022353, 9759264753603, 205434011254501, 4544894700204001, 107346788357502273, 2657668122191037763, 69701762677026498733, 1909106308252976007081

Offset: 0

Author

Seiichi Manyama, Nov 29 2023

Keywords

• nonn

Crossrefs

Cf. A000272, A367748, A367749, A367751.

Cf. A127680, A138292.

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]/((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) / (floor(k/2)! * (n-1-k)!).