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A051621 a(n) = (4*n+9)(!^4)/9(!^4), related to A007696(n+1) ((4*n+1)(!^4) quartic, or 4-factorials). 4
1, 13, 221, 4641, 116025, 3364725, 111035925, 4108329225, 168441498225, 7579867420125, 371413503586125, 19684915690064625, 1122040194333683625, 68444451854354701125, 4448889370533055573125, 306973366566780834545625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row m=9 of the array A(5; m,n) := ((4*n+m)(!^4))/m(!^4), m >= 0, n >= 0.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..363

FORMULA

a(n) = ((4*n+9)(!^4))/9(!^4) = A007696(n+3)/(5*9).

E.g.f.: 1/(1-4*x)^(13/4).

MATHEMATICA

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 12, 5!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)

With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(13/4), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-4*x)^(13/4))) \\ G. C. Greubel, Aug 15 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(13/4))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018

CROSSREFS

Cf. A047053, A007696(n+1), A000407, A034176(n+1), A034177(n+1), A051617-A051622 (rows m=0..10).

Sequence in context: A059525 A086147 A015253 * A173427 A051180 A143832

Adjacent sequences:  A051618 A051619 A051620 * A051622 A051623 A051624

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified August 25 05:45 EDT 2019. Contains 326323 sequences. (Running on oeis4.)