A367720 E.g.f. satisfies A(x) = exp(x*A(x^4)).

1, 1, 1, 1, 1, 121, 721, 2521, 6721, 196561, 3659041, 29993041, 159762241, 1686639241, 60298558321, 987112886761, 9315623640961, 76611297104161, 2454331471018561, 69805324167893281, 1086439146068753281, 62621251106366355481, 1358219171406244427281

Offset

0,6

Comments

This sequence is different from A354554.

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/4)} (4*k+1) * a(k) * a(n-1-4*k) / (k! * (n-1-4*k)!).

Prog

(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)\4, (4*j+1)*v[j+1]*v[i-4*j]/(j!*(i-1-4*j)!))); v;

Crossrefs

Cf. A138292, A367719.

Cf. A354554.

Sequence in context: A190877 A361636 A354554 * A293566 A293507 A356630

Adjacent sequences: A367717 A367718 A367719 * A367721 A367722 A367723

Keyword

nonn

Author

Seiichi Manyama, Nov 28 2023

Status

approved