A051690 a(n) = (5*n+9)(!^5)/9(!^5), related to A034301 ((5*n+2)(!^5) quintic, or 5-factorials).

1, 14, 266, 6384, 185136, 6294624, 245490336, 10801574784, 529277164416, 28580966878464, 1686277045829376, 107921730933080064, 7446599434382524416, 551048358144306806784, 43532820293400237735936

Offset

0,2

Comments

Row m=9 of the array A(6; m,n) := ((5*n+m)(!^5))/m(!^5), m >= 0, n >= 0.

Links

G. C. Greubel, Table of n, a(n) for n = 0..352

Formula

a(n) = ((5*n+9)(!^5))/9(!^5) = A034301(n+2)/9.

E.g.f.: 1/(1-5*x)^(14/5).

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 13, 5!, 5}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 5*x)^(14/5), {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Aug 15 2018 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-5*x)^(14/5))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-5*x)^14/5))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018

Crossrefs

Cf. A052562, A008548(n+1), A034323(n+1), A034300(n+1), A034301(n+1), A034325(n+1), A051687-A051691 (rows m=0..10).

Sequence in context: A205467 A216986 A138560 * A048668 A001820 A211900

Adjacent sequences: A051687 A051688 A051689 * A051691 A051692 A051693

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved