A057693 -id:A057693 - cp's OEIS frontend

A211371 The number of indecomposable n-permutations that have only cycles of length 3 or less.

0, 1, 1, 3, 7, 29, 131, 585, 3083, 17089, 97987, 607977, 3926731, 26344001, 185908739, 1358432937, 10279616891, 80819893393, 655374770131, 5482528852761, 47329769940331, 420061520283617, 3832533793409027, 35926633641149865, 345280194806563931

Offset: 0

Geoffrey Critzer, May 11 2012

nonn

			a(4) = 7 because we have: 2431, 3241, 3412, 4132, 4213, 4231, 4321.

Cf. A057693, A003319, A140456.

nn = 20; a = x + x^2/2 + x^3/3; b = Total[Range[0, nn]! CoefficientList[Series[Exp[a], {x, 0, nn}], x]* x^Range[0, nn]]; CoefficientList[Series[1 - 1/b, {x, 0, nn}], x]

G.f.: 1-1/A(x) where A(x) is the o.g.f. for A057693.

A324591 E.g.f.: exp(2 * (x + x^2 / 2 + x^3 / 3)).

Original entry on oeis.org

1, 2, 6, 24, 108, 552, 3144, 19392, 129168, 920736, 6958944, 55582848, 466824384, 4104798336, 37688879232, 360236187648, 3575154053376, 36768528142848, 391060780180992, 4293782854170624, 48597548604926976, 566152604314232832, 6780179847538722816, 83375209195856216064

Offset: 0

Ilya Gutkovskiy, Nov 20 2020

nonn

Cf. A000898, A057693.

nmax = 23; CoefficientList[Series[Exp[2 (x + x^2/2 + x^3/3)], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[1] = 2; a[2] = 6; a[n_] := a[n] = 2 (a[n - 1] + (n - 1) a[n - 2] + (n - 1) (n - 2) a[n - 3]); Table[a[n], {n, 0, 23}]

my(x='x+O('x^30)); Vec(serlaplace(exp(2*(x + x^2/2 + x^3/3)))) \\ Michel Marcus, Nov 21 2020

D-finite recurrence: a(n) = 2 * (a(n-1) + (n-1) * a(n-2) + (n-1) * (n-2) * a(n-3)).

a(n) = Sum_{k=0..n} binomial(n,k) * A057693(k) * A057693(n-k).

cp's OEIS Frontend

A211371 The number of indecomposable n-permutations that have only cycles of length 3 or less.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula