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URL: https://oeis.org/A383450

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A383450
2nd diagonal (from right) in A104978.
3
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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 02 2025
STATUS
approved