A386298 a(n) = 1 + Sum_{k=0..n-1} 2^k * binomial(n-1,k) * a(k) * a(n-1-k).

1, 2, 7, 52, 721, 17594, 754063, 58139188, 8321310193, 2272187953346, 1206524396886823, 1260788083530821380, 2611061273843639666401, 10760136322351992470924570, 88437432027319862460463145551, 1451522912694521425631922482171812, 47608493474799808182534348919785356065

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

E.g.f. A(x) satisfies A'(x) = exp(x) + A(x) * A(2*x).

Prog

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

Crossrefs

Cf. A054687, A386299, A386300.

Cf. A345104, A348857.

Sequence in context: A138737 A216086 A210856 * A046662 A237195 A275597

Adjacent sequences: A386295 A386296 A386297 * A386299 A386300 A386301

Keyword

nonn

Author

Seiichi Manyama, Jul 17 2025

Status

approved