A355219 a(n) = Sum_{k>=1} (4*k - 2)^n / 2^k.

1, 6, 68, 1176, 27152, 783456, 27126848, 1095801216, 50589024512, 2627443262976, 151623974601728, 9624874873952256, 666516443992297472, 50002158357801885696, 4039720490206565777408, 349685083067909962039296, 32287291853754803207340032, 3167488677197974581176303616

Offset

0,2

Links

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

Formula

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

a(0) = 1; a(n) = 2^n + Sum_{k=1..n} binomial(n,k) * 4^k * a(n-k).

a(n) = Sum_{k=0..n} binomial(n,k) * 2^(n+k) * A000670(k).

a(n) ~ n! * 2^(2*n - 1/2) / log(2)^(n+1). - Vaclav Kotesovec, Jun 24 2022

Mathematica

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

Crossrefs

Cf. A000629, A000670, A007047, A080253, A285067, A328183, A355218, A355220.

Sequence in context: A370938 A349557 A140606 * A014505 A363396 A274722

Adjacent sequences: A355216 A355217 A355218 * A355220 A355221 A355222

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 24 2022

Status

approved