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A052695 Expansion of e.g.f. (2-5*x)/((1-x)*(1-4*x)). 1
2, 5, 34, 390, 6168, 123000, 2949840, 82580400, 2642451840, 95127177600, 3805076217600, 167423233824000, 8036313786547200, 417888298219392000, 23401744438751078400, 1404104662402041600000, 89862698330962292736000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..360

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 644

FORMULA

E.g.f.: (2-5*x)/((1-x)*(1-4*x)).

D-finite Recurrence: a(0)=2, a(1)=5, a(n) = 5*n*a(n-1) - 4*n*(n-1)*a(n-2).

a(n) = (4^n + 1)*n!.

MAPLE

spec := [S, {S=Union(Sequence(Z), Sequence(Union(Z, Z, Z, Z)))}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(2-5x)/((1-4x)(1-x)), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Sep 12 2020 *)

PROG

(SageMath) [factorial(n)*(4^n +1) for n in (0..30)] # G. C. Greubel, May 31 2022

CROSSREFS

Cf. A000142, A052539.

Sequence in context: A357446 A356772 A307143 * A184360 A283111 A206830

Adjacent sequences: A052692 A052693 A052694 * A052696 A052697 A052698

KEYWORD

easy,nonn

AUTHOR

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

STATUS

approved

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Last modified November 26 21:15 EST 2022. Contains 358362 sequences. (Running on oeis4.)