A337553 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (4*k-3) * a(n-k).

1, 1, 7, 45, 439, 5157, 73455, 1217101, 23066311, 491680437, 11645898655, 303422639517, 8624098330359, 265546702327813, 8805478883825359, 312844282877905389, 11855836533424581415, 477380986427269453653, 20352680600044759742463, 915923521948522369041469

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f.: 1 / (exp(x) * (3 - 4*x) - 2).

a(n) ~ n! * c * 2^(2*n+1) / ((1-c) * (3 - 4*c)^(n+1)), where c = -LambertW(-exp(-3/4)/2). - Vaclav Kotesovec, Aug 31 2020

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (4 k - 3) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(Exp[x] (3 - 4 x) - 2), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (3 - 4*x) - 2)))} \\ Andrew Howroyd, Aug 31 2020

Crossrefs

Cf. A000354, A001907, A337552, A337554.

Sequence in context: A001266 A071971 A370253 * A006680 A197796 A197856

Adjacent sequences: A337550 A337551 A337552 * A337554 A337555 A337556

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 31 2020

Status

approved