A034834 One seventh of sept-factorial numbers.

1, 14, 294, 8232, 288120, 12101040, 592950960, 33205253760, 2091930986880, 146435169081600, 11275508019283200, 947142673619788800, 86189983299400780800, 8446618363341276518400, 886894928150834034432000, 99332231952893411856384000, 11820535602394316010909696000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..335
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A045754, A034829, A034830, A034831, A034832, A034833, A051188.

Programs

Magma

[7^(n-1)*Factorial(n): n in [1..30]]; // G. C. Greubel, Feb 22 2018

Mathematica

Table[7^(n-1)*n!, {n,1,30}] (* or *) Drop[With[{nn = 50},CoefficientList[ Series[x/(1-7*x), {x, 0, nn}], x]*Range[0, nn]!], 1] (* G. C. Greubel, Feb 22 2018 *)

PARI

my(x='x+O('x^30)); Vec(serlaplace(x/(1-7*x))) \\ G. C. Greubel, Feb 22 2018

Formula

7*a(n) = (7*n)(!^7) = Product_{j=1..n} 7*j = 7^n*n!.

E.g.f.: x/(1-7*x).

a(n) = A051188(n)/7.

From Amiram Eldar, Jan 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 7*(exp(1/7)-1).

Sum_{n>=1} (-1)^(n+1)/a(n) = 7*(1-exp(-1/7)). (End)

Extensions

More terms from G. C. Greubel, Feb 22 2018