A093965 Number of functions of [n] to [n] that simultaneously avoid the patterns 112 and 221.

1, 4, 21, 124, 825, 6186, 51961, 484968, 4988241, 56117710, 685883121, 9053657196, 128397320233, 1947359356866, 31457343457065, 539268744978256, 9778739908939041, 187018400758459158, 3762370179964296001, 79427814910357360020, 1755772750650004800441

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

a(n) = A093966(n, n).

From Vaclav Kotesovec, Nov 20 2012: (Start)

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

Recurrence: (n-1)*a(n) = n*(n+1)*a(n-1) - (n-1)*n*a(n-2) for n>2.

a(n) ~ n!*n*(e-1). (End)

Mathematica

Rest[CoefficientList[Series[x(E^x-x)/(1-x)^2, {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Nov 20 2012 *)

Prog

(PARI)  my(x='x+O('x^66)); Vec(serlaplace(x*(exp(x)-x)/(1-x)^2)) \\ Joerg Arndt, May 11 2013
(Magma) [n le 2 select 4^(n-1) else n*((n+1)*Self(n-1) - (n-1)*Self(n-2))/(n-1): n in [1..30]]; // G. C. Greubel, Dec 29 2021
(Sage) [factorial(n)*( x*(exp(x) -x)/(1-x)^2 ).series(x, n+1).list()[n] for n in (1..30)] # G. C. Greubel, Dec 29 2021

Crossrefs

Cf. A093966.

Sequence in context: A101478 A153291 A244062 * A370545 A366115 A195262

Adjacent sequences: A093962 A093963 A093964 * A093966 A093967 A093968

Keyword

nonn

Author

Ralf Stephan, Apr 20 2004

Extensions

Name changed by Olivier Gérard, Aug 06 2016

Status

approved