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A093965 Number of functions of [n] to [n] that simultaneously avoid the patterns 112 and 221. 2
1, 4, 21, 124, 825, 6186, 51961, 484968, 4988241, 56117710, 685883121, 9053657196, 128397320233, 1947359356866, 31457343457065, 539268744978256, 9778739908939041, 187018400758459158, 3762370179964296001, 79427814910357360020, 1755772750650004800441 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(n,n), where T is array in A093966.

LINKS

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

FORMULA

From Vaclav Kotesovec, Nov 20 2012: (Start)

E.g.f.: (exp(x)*x-x^2)/(x-1)^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[(E^x*x-x^2)/(x-1)^2, {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Nov 20 2012 *)

PROG

(PARI)  x='x+O('x^66); Vec(serlaplace((exp(x)*x-x^2)/(x-1)^2)) \\ Joerg Arndt, May 11 2013

CROSSREFS

Sequence in context: A101478 A153291 A244062 * A195262 A162480 A275758

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

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Last modified September 21 15:47 EDT 2021. Contains 347598 sequences. (Running on oeis4.)