A383451 3nd 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

Author

N. J. A. Sloane, May 02 2025

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A104987.

Programs

Maple

From Peter Luschny, May 04 2025:  (Start)
a := n -> (3*n + 6)!/(6*n!*(3 + 2*n + 1)!): seq(a(n), n = 0..23);
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);  (End)

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)