A383450 2nd diagonal (from right) in A104978.

2, 21, 180, 1430, 10920, 81396, 596904, 4326300, 31081050, 221760825, 1573537680, 11114897976, 78215948720, 548652722520, 3838040704080, 26784871943928, 186537501038070, 1296717366119175, 8999440181955300, 62366467037593950, 431633967218324640, 2983755440056831440, 20603495011611002400, 142131208489591604400

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 + 4)! / (2*n!*(3 + 2*n)!).

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

a(n) ~ 3^(3*n+9/2)*2^(-2n-5)*sqrt(n/Pi). - Stefano Spezia, Sep 09 2025

Maple

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

Mathematica

A383450[n_] := (3*n + 4)!/(2*n!*(3 + 2*n)!);
Array[A383450, 25, 0] (* Paolo Xausa, Mar 22 2026 *)

Crossrefs

Cf. A104978, A104987, A383451.

Sequence in context: A112673 A389840 A263435 * A202028 A265167 A037749

Adjacent sequences: A383447 A383448 A383449 * A383451 A383452 A383453

Keyword

nonn

Author

N. J. A. Sloane, May 02 2025

Status

approved