A355220 a(n) = Sum_{k>=1} (4*k - 1)^n / 2^k.

1, 7, 81, 1399, 32289, 931687, 32259441, 1303134679, 60160827969, 3124574220487, 180312309395601, 11445969681199159, 792626097462398049, 59462922484586318887, 4804064349575887075761, 415847988794676360818839, 38396277196654611908582529, 3766800071614388562865514887

Offset

0,2

Links

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

Formula

E.g.f.: exp(3*x) / (2 - exp(4*x)).

a(0) = 1; a(n) = 3^n + Sum_{k=1..n} binomial(n,k) * 4^k * a(n-k).

a(n) = Sum_{k=0..n} binomial(n,k) * 3^(n-k) * 4^k * A000670(k).

a(n) ~ n! * 2^(2*n - 1/4) / log(2)^(n+1). - Vaclav Kotesovec, Jun 24 2022

Mathematica

nmax = 17; CoefficientList[Series[Exp[3 x]/(2 - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = 3^n + Sum[Binomial[n, k] 4^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 17}]

Crossrefs

Cf. A000629, A000670, A080253, A259533, A285067, A328183, A355218, A355219.

Sequence in context: A369024 A371027 A058575 * A285062 A253265 A338684

Adjacent sequences: A355217 A355218 A355219 * A355221 A355222 A355223

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 24 2022

Status

approved