A051619 a(n) = (4*n+7)(!^4)/7(!^4), related to A034176(n+1) ((4*n+3)(!^4) quartic, or 4-factorials).

1, 11, 165, 3135, 72105, 1946835, 60351885, 2112315975, 82380323025, 3542353890075, 166490632833525, 8491022274509775, 467006225098037625, 27553367280784219875, 1735862138689405852125, 116302763292190192092375

Offset

0,2

Comments

Row m=7 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+7)(!^4))/7(!^4) = A034176(n+2)/7.

E.g.f.: 1/(1-4*x)^(11/4).

Mathematica

s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 10, 5!, 4}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 08 2008 *)
With[{nn = 30}, CoefficientList[Series[1/(1 - 4*x)^(11/4), {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)^(11/4))) \\ G. C. Greubel, Aug 15 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(1/(1-4*x)^(11/4))); [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: A141876 A174364 A229963 * A261504 A142513 A075141

Adjacent sequences: A051616 A051617 A051618 * A051620 A051621 A051622

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved