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A051605 a(n) = (3*n+5)!!!/5!!!. 6
1, 8, 88, 1232, 20944, 418880, 9634240, 250490240, 7264216960, 232454942720, 8135922995200, 309165073817600, 12675768026521600, 557733793166950400, 26213488278846668800, 1310674413942333440000, 69465743938943672320000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Related to A008544(n+1) ((3*n+2)!!! triple factorials).

Row m=5 of the array A(4; m,n) := ((3*n+m)(!^3))/m(!^3), m >= 0, n >= 0.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..378

FORMULA

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

E.g.f.: 1/(1-3*x)^(8/3).

a(n) = 3^n*(n+5/3)!/(5/3)! - Paul Barry, Sep 04 2005

a(n) = (3*n+5)*a(n-1). - R. J. Mathar, Nov 13 2012

MATHEMATICA

RecurrenceTable[{a[0]==1, a[n]==(3n+5)a[n-1]}, a, {n, 20}] (* Harvey P. Dale, Oct 19 2013 *)

With[{nn = 30}, CoefficientList[Series[1/(1 - 3*x)^(8/3), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)

PROG

(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-3*x)^(8/3))) \\ G. C. Greubel, Aug 15 2018

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-3*x)^(8/3))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018

CROSSREFS

Cf. A032031, A007559(n+1), A034000(n+1), A034001(n+1), A051604 (rows m=0..4).

Sequence in context: A115864 A036917 A003497 * A271268 A006750 A082783

Adjacent sequences:  A051602 A051603 A051604 * A051606 A051607 A051608

KEYWORD

easy,nonn

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified June 20 20:08 EDT 2021. Contains 345231 sequences. (Running on oeis4.)