A352859 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(n,k+1) * 2^k * a(k).

1, 1, 4, 25, 280, 5665, 211516, 14907673, 2021820016, 535262714881, 279317901141172, 289064917007756761, 595455410823115765768, 2446703815513439818406305, 20077597428602000393057306476, 329252263598282049972950683567705, 10794203801863458962317873561872563680

Offset: 0

Author

Ilya Gutkovskiy, Apr 06 2022

Keywords

• nonn

Crossrefs

Cf. A040027, A126443, A351756, A352860.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k + 1] 2^k a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; A[] = 0; Do[A[x] = 1 + x A[2 x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

G.f. A(x) satisfies: A(x) = 1 + x * A(2*x/(1 - x)) / (1 - x)^2.

a(n) ~ c * 2^(n*(n-1)/2), where c = 8.12511731924148105991770742530352144084320407825344... - Vaclav Kotesovec, Apr 07 2022