OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 06 2019
STATUS
approved