OFFSET
1,2
LINKS
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
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 *)
PROG
(PARI) vector(21, n, prod(j=0, n-1, 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
(Sage) [product( (10*j+1) for j in (0..n-1)) for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> Product([0..n-1], j-> 10*j+1) ); # G. C. Greubel, Nov 11 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved