A035308 Expansion of 1/(1-100*x)^(1/10), related to deca-factorial numbers A045757.

1, 10, 550, 38500, 2983750, 244667500, 20796737500, 1812287125000, 160840482343750, 14475643410937500, 1317283550395312500, 120950580536296875000, 11187928699607460937500, 1041337978963463671875000, 97439482317295529296875000, 9159311337825779753906250000

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500
• Armin Straub, Victor H. Moll, and Tewodros Amdeberhan, The p-adic valuation of k-central binomial coefficients, Acta Arith. 140 (1) (2009), 31-41, eq (1.10).
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A045757, A035024, A004993, A000984, A004987, A256191.

Programs

Mathematica

CoefficientList[Series[1/(1-100*x)^(1/10), {x, 0, 20}], x] (* Amiram Eldar, Aug 18 2025 *)

Formula

a(n) = 10^n*A045757(n)/n!, n >= 1, where A045757(n) = (10*n-9)(!^10) = Product_{j=1..n} (10*j-9).

G.f.: (1-100*x)^(-1/10).

a(n) ~ 10^(2*n) * n^(-9/10) / Gamma(1/10). - Amiram Eldar, Aug 18 2025