A035278 One ninth of deca-factorial numbers.

1, 19, 551, 21489, 1052961, 62124699, 4286604231, 338641734249, 30139114348161, 2983772320467939, 325231182931005351, 38702510768789636769, 4992623889173863143201, 693974720595166976904939, 103402233368679879558835911, 16440955105620100849854909849

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..320

Index entries for sequences related to factorial numbers.

Formula

9*a(n) = (10*n-1)(!^10) = Product_{j=1..n} (10*j-1).

E.g.f.: (-1+(1-10*x)^(-9/10))/9.

a(n) = (Pochhammer(9/10,n) * 10^n)/9.

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

Maple

seq( mul(10*j-1, j=1..n)/9, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[10^n*Pochhammer[9/10, n]/9, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

Prog

(PARI) vector(20, n, prod(j=1, n, 10*j-1)/9 ) \\ G. C. Greubel, Nov 11 2019
(Magma) [(&*[10*j-1: j in [1..n]])/9: n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) [product( (10*j-1) for j in (1..n))/9 for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) List([1..20], n-> Product([1..n], j-> 10*j-1)/9 ); # G. C. Greubel, Nov 11 2019

Crossrefs

Cf. A045757, A035265, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.

Sequence in context: A309313 A158211 A278184 * A092611 A008990 A012845

Adjacent sequences: A035275 A035276 A035277 * A035279 A035280 A035281

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved