A386272 Expansion of 1/(1 - 49*x)^(3/7).

1, 21, 735, 29155, 1224510, 53143734, 2356038874, 106021749330, 4823989594515, 221367522503855, 10227179539678101, 475098976797773601, 22171285583896101380, 1038639455430209672340, 48816054405219854599980, 2300863364299362480145724, 108715793963144877186885459

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (-49)^n * binomial(-3/7,n).

a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+3).

a(n) = 7^n * Product_{k=1..n} (7 - 4/k).

D-finite with recurrence n*a(n) + 7*(-7*n+4)*a(n-1) = 0. - R. J. Mathar, Jul 20 2025

a(n) ~ cos(Pi/14) * Gamma(4/7) * 49^n / (n^(4/7) * Pi). - Amiram Eldar, Nov 06 2025

Mathematica

a[n_] := (-49)^n * Binomial[-3/7, 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)^(3/7))

Crossrefs

Cf. A034835, A216703, A386271, A386273, A386274.

Cf. A049381, A216702.

Cf. A220609, A232735.

Sequence in context: A297504 A250059 A250060 * A078791 A201069 A143002

Adjacent sequences: A386269 A386270 A386271 * A386273 A386274 A386275

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 17 2025

Status

approved