A394523 E.g.f. A(x) satisfies A(x) = 1/(1 - 4*x*A(x)^3)^(1/4).

1, 1, 11, 252, 8925, 430080, 26277615, 1946992320, 169660984185, 17003918131200, 1927077560082675, 243695697227136000, 34019980658006267925, 5196649855071132057600, 862198242648765371724375, 154404750988666446428160000, 29685365313948255992984528625, 6098434519783164467918929920000

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = 4^n * n! * binomial((7*n+1)/4,n)/(7*n+1).

Mathematica

a[n_]:=If[n==0, 1, Product[(7*n+1-4*k), {k, 0, n-1}]/(7*n+1)]; Table[a[n], {n, 0, 18}] (* Vincenzo Librandi, Mar 28 2026 *)

Prog

(PARI) a(n) = 4^n*n!*binomial((7*n+1)/4, n)/(7*n+1);
(Magma) [n eq 0 select 1 else (4^n*&*[((7*n+1)/4-k): k in [0..n-1] ])/(7*n+1): n in [0..23]]; // Vincenzo Librandi, Mar 28 2026

Crossrefs

Cf. A394494, A394522, A394524.

Sequence in context: A190680 A377327 A089298 * A274129 A346896 A012154

Adjacent sequences: A394520 A394521 A394522 * A394524 A394525 A394526

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 23 2026

Status

approved