A392372 E.g.f. A(x) satisfies A(x) = exp( -x * d/dx log(1 - x*A(x)) ).

1, 1, 7, 106, 2693, 101136, 5208427, 350079136, 29655632169, 3084806690560, 386157558367151, 57239257050526464, 9913670289956500333, 1983894690594669669376, 454331789822164009288275, 118077198411780842498154496, 34569903816081852421748189393, 11327237659616427357082928676864

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..252

Formula

E.g.f. A(x) satisfies A(x) = exp( x * (A(x) + x*d/dx A(x))/(1 - x*A(x)) ).

a(0) = 1; a(n) = Sum_{i=0..n-1} (i^2+2*n-1) * binomial(n-1,i) * a(i)*a(n-1-i) + Sum_{i, j, k>=0 and i+j+k=n-2} (i*j+i-j^2-2*j) * (n-1)!/(i!*j!*k!) * a(i)*a(j)*a(k).

a(n) ~ c * n^(2*n + 3) / exp(2*n), where c = 2.034311414558208... - Vaclav Kotesovec, Apr 06 2026

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j^2+2*i-1)*binomial(i-1, j)*v[j+1]*v[i-j])+sum(j=0, i-2, sum(k=0, i-2-j, (j*k+j-k^2-2*k)*(i-1)!/(j!*k!*(i-2-j-k)!)*v[j+1]*v[k+1]*v[i-1-j-k]))); v;

Crossrefs

Cf. A000262, A052873.

Sequence in context: A213863 A231899 A384689 * A188407 A075021 A138963

Adjacent sequences: A392369 A392370 A392371 * A392373 A392374 A392375

Keyword

nonn

Author

Seiichi Manyama, Apr 06 2026

Status

approved