A337011 a(n) = 2^n * exp(-1/2) * Sum_{k>=0} (k + 2)^n / (2^k * k!).

1, 5, 27, 159, 1025, 7221, 55307, 457631, 4065569, 38566021, 388757083, 4146851583, 46636281185, 551163837685, 6825500514059, 88341860285631, 1192267628956353, 16743728349797765, 244221140242647579, 3693367920926321375, 57821628101627115329

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..513

Formula

E.g.f.: exp(4*x + (exp(2*x) - 1) / 2).

a(0) = 1; a(n) = 5 * a(n-1) + Sum_{k=2..n} binomial(n-1,k-1) * 2^(k-1) * a(n-k).

a(n) = Sum_{k=0..n} binomial(n,k) * 4^(n-k) * A004211(k).

Maple

E:= exp(4*x+exp(2*x)/2-1/2):
S:= series(E, x, 31):
seq(coeff(S, x, n)*n!, n=0..30); # Robert Israel, Aug 14 2020

Mathematica

nmax = 20; CoefficientList[Series[Exp[4 x + (Exp[2 x] - 1)/2], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = 5 a[n - 1] + Sum[Binomial[n - 1, k - 1] 2^(k - 1) a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 20}]

Crossrefs

Cf. A004211, A007405, A045379, A337010.

Sequence in context: A153233 A084076 A355252 * A081924 A366176 A368317

Adjacent sequences: A337008 A337009 A337010 * A337012 A337013 A337014

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 11 2020

Status

approved