A386507 a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * k^4 * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 3, 151, 49525, 63641021, 239036610181, 2170214958201445, 41702857906969051017, 1537709560908537888618409, 100904503302575334820438217641, 11100605398391683050596962755215561, 1950420777626865443224119613333235611309, 525796384523344023260217345195483215249534941

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

E.g.f. A(x) satisfies A(x) = exp( x + x*Sum_{k=1..4} Stirling2(4,k) * x^k * (d^k/dx^k A(x)) ).

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*j^4*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143925, A386505, A386506, A386508, A386509.

Cf. A385941, A386445.

Sequence in context: A157578 A137802 A100203 * A287319 A189248 A209393

Adjacent sequences: A386504 A386505 A386506 * A386508 A386509 A386510

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2025

Status

approved