A386274 Expansion of 1/(1 - 49*x)^(5/7).

1, 35, 1470, 65170, 2965235, 136993857, 6393046660, 300473193020, 14197358370195, 673585780452585, 32062683149543046, 1530264423046372650, 73197648235718158425, 3507856526988647130675, 168377113295455062272400, 8093326579068206659893360, 389491341617657445507367950

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..592

Formula

a(n) = (-49)^n * binomial(-5/7,n).

a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+5).

a(n) = 7^n * Product_{k=1..n} (7 - 2/k).

D-finite with recurrence n*a(n) + 7*(-7*n+2)*a(n-1) = 0. - R. J. Mathar, Jul 30 2025

a(n) ~ cos(3*Pi/14) * Gamma(2/7) * 49^n / (n^(2/7) * Pi). - Amiram Eldar, Nov 06 2025

Mathematica

CoefficientList[Series[1/(Surd[1-49x, 7])^5, {x, 0, 20}], x] (* Harvey P. Dale, Aug 01 2025 *)
a[n_] := (-49)^n * Binomial[-5/7, n]; Array[a, 20, 0] (* Amiram Eldar, Nov 06 2025 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(1/(1-49*x)^(5/7))

Crossrefs

Cf. A034835, A216703, A220605, A386271, A386272, A386273.

Sequence in context: A195617 A249885 A135923 * A180883 A130005 A199362

Adjacent sequences: A386271 A386272 A386273 * A386275 A386276 A386277

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 17 2025

Status

approved