A383451 3rd diagonal (from right) in A104978.

5, 84, 990, 10010, 92820, 813960, 6864396, 56241900, 450675225, 3548173200, 27536909400, 211183061544, 1603426948760, 12070359895440, 90193956545880, 669621798598200, 4943243777508855, 36308086251336900, 265483485367681350, 1933360478165412450, 14028103934595550800, 101447684961932268960, 731424072912190585200, 5258854714114889362800

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

N. J. Wildberger and Dean Rubine, A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode, Amer. Math. Monthly (2025). See table on page 12.

Formula

From Peter Luschny, May 04 2025: (Start)

a(n) = (3*n + 6)!/(6*n!*(3 + 2*n + 1)!).

a(n) = [x^n] 5*hypergeom([7/3, 8/3], [5/2], (27*x)/4). (End)

a(n) ~ 3^(3*n+7/2)*2^(-2*n-9)*(137+72*n)*sqrt(n/Pi). - Stefano Spezia, Sep 09 2025

Maple

a := n -> (3*n + 6)!/(6*n!*(3 + 2*n + 1)!): seq(a(n), n = 0..23); # Peter Luschny, May 04 2025
# Alternative:
gf := 5*hypergeom([7/3, 8/3], [5/2], (27*x)/4):
ser := series(gf, x, 25): seq(coeff(ser, x, k), k = 0..23); # Peter Luschny, May 04 2025

Mathematica

A383451[n_] := (3*n + 6)!/(6*n!*(3 + 2*n + 1)!);
Array[A383451, 25, 0] (* Paolo Xausa, Mar 22 2026 *)

Crossrefs

Cf. A104978, A104987, A383450.

Sequence in context: A359110 A187587 A006471 * A258391 A061628 A193369

Adjacent sequences: A383448 A383449 A383450 * A383452 A383453 A383454

Keyword

nonn

Author

N. J. A. Sloane, May 02 2025

Status

approved