A367751 E.g.f. satisfies A(x) = exp(x * (1 + x + x^2 + x^3 + x^4) * A(x^5)).

1, 1, 3, 13, 73, 501, 4051, 37633, 394353, 4596553, 58941091, 844031541, 12949163833, 213873687613, 3782022682803, 71267635330921, 1439160383457121, 30612704101371153, 686728250047551043, 16198763975779425373, 400727742254252310441

Offset: 0

Author

Seiichi Manyama, Nov 29 2023

Keywords

• nonn

Crossrefs

Cf. A367747, A367748, A367749.

Cf. A367654.

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\5+1]*v[i-j]/((j\5)!*(i-1-j)!))); v;

Formula

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