A328183 Expansion of e.g.f. 1 / (2 - exp(4*x)).

1, 4, 48, 832, 19200, 553984, 19181568, 774848512, 35771842560, 1857882947584, 107214340620288, 6805814291464192, 471298297319915520, 35356865248765149184, 2856513752723261227008, 247264693517100223823872, 22830563015939200206766080, 2239752722978295095737974784

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) = Sum_{k>=0} (4*k)^n / 2^(k + 1).

a(n) = 4^n * A000670(n).

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      a(n-j)*binomial(n, j)*4^j, j=1..n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Oct 06 2019

Mathematica

nmax = 17; CoefficientList[Series[1/(2 - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[4^k Binomial[n, k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]
Table[2^(2 n - 1) HurwitzLerchPhi[1/2, -n, 0], {n, 0, 17}]

Crossrefs

Cf. A000670, A216794, A328182.

Sequence in context: A371677 A369537 A371658 * A047711 A089448 A167141

Adjacent sequences: A328180 A328181 A328182 * A328184 A328185 A328186

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 06 2019

Status

approved