A053100 a(n) = ((6*n+7)(!^6))/7, related to A008542 ((6*n+1)(!^6) sextic, or 6-factorials).

1, 13, 247, 6175, 191425, 7082725, 304557175, 14923301575, 820781586625, 50067676784125, 3354534344536375, 244881007151155375, 19345599564941274625, 1644375963020008343125, 149638212634820759224375

Offset

0,2

Comments

Row m=7 of the array A(7; m,n) := ((6*n+m)(!^6))/m(!^6), m >= 0, n >= 0.

Links

G. C. Greubel, Table of n, a(n) for n = 0..344

Formula

a(n) = ((6*n+7)(!^6))/7(!^6) = A008542(n+2)/7.

E.g.f.: 1/(1-6*x)^(13/6).

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 12, 5!, 6}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn=20}, CoefficientList[Series[1/(1-6x)^(13/6), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Apr 20 2015 *)

Prog

(PARI) x='x+O('x^30); Vec(serlaplace(1/(1-6*x)^(13/6))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-6*x)^(13/6))); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 15 2018

Crossrefs

Cf. A047058, A008542(n+1), A034689(n+1), A034723(n+1), A034724(n+1), A034787(n+1), A034788(n+1), this sequence, A053101, A053102, A053103 (rows m=0..10).

Sequence in context: A049665 A196665 A027400 * A320308 A219059 A218315

Adjacent sequences: A053097 A053098 A053099 * A053101 A053102 A053103

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved