A386273 Expansion of 1/(1 - 49*x)^(4/7).

1, 28, 1078, 45276, 1980825, 88740960, 4037713680, 185734829280, 8613452707860, 401961126366800, 18851976826602920, 887756726925482960, 41946505347229069860, 1987619022607162079520, 94411903573840198777200, 4494006610114793461794720, 214307940219849213209335710

Offset

0,2

Links

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

Formula

a(n) = (-49)^n * binomial(-4/7,n).

a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+4).

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

D-finite with recurrence n*a(n) + 7*(-7*n+3)*a(n-1) = 0. - R. J. Mathar, Jul 20 2025

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

Mathematica

a[n_] := (-49)^n * Binomial[-4/7, 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)^(4/7))

Crossrefs

Cf. A034835, A216703, A386271, A386272, A386274.

Cf. A220608, A232735.

Sequence in context: A162006 A365029 A370358 * A025753 A160312 A132503

Adjacent sequences: A386270 A386271 A386272 * A386274 A386275 A386276

Keyword

nonn,easy

Author

Seiichi Manyama, Jul 17 2025

Status

approved