A045757 10-factorial numbers.

1, 11, 231, 7161, 293601, 14973651, 913392711, 64850882481, 5252921480961, 478015854767451, 48279601331512551, 5359035747797893161, 648443325483545072481, 84946075638344404495011, 11977396665006561033796551, 1808586896415990716103279201, 291182490322974505292627951361

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..323
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A035265, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.

Cf. A008542, A048176.

Programs

GAP

List([1..20], n-> Product([0..n-1], j-> 10*j+1) ); # G. C. Greubel, Nov 11 2019

Magma

[(&*[10*j+1: j in [0..n-1]]): n in [1..20]]; // G. C. Greubel, Nov 11 2019

Maple

G(x):=-1+(1-10*x)^(-1/10): f[0]:=G(x): for n from 1 to 29 do f[n]:=diff(f[n-1],x) od: x:=0: seq(f[n],n=1..14); # Zerinvary Lajos, Apr 03 2009
seq(mul(10*j+1, j = 0..n-1), n = 1..20); # G. C. Greubel, Nov 11 2019

Mathematica

FoldList[Times,10*Range[0,20]+1] (* Harvey P. Dale, Dec 02 2016 *)

PARI

vector(21, n, prod(j=0,n-1, 10*j+1) ) \\ G. C. Greubel, Nov 11 2019

Sage

[product( (10*j+1) for j in (0..n-1)) for n in (1..20)] # G. C. Greubel, Nov 11 2019

Formula

a(n) = Pochhammer(1/10,n)*10^n.

a(n+1) = (10*n+1)(!^10) = Product_{k=0..n} (10*k+1), n >= 0.

E.g.f.: -1 + (1-10*x)^(-1/10).

Sum_{n>=1} 1/a(n) = (e/10^9)^(1/10)*(Gamma(1/10) - Gamma(1/10, 1/10)). - Amiram Eldar, Dec 22 2022