A383632 Expansion of 1/( Product_{k=0..8} (1 - (9*k+1) * x) )^(1/9).

1, 37, 1639, 80623, 4257424, 236721412, 13688641144, 816291120808, 49895692924132, 3112177949225236, 197407027057353724, 12699858803178669148, 826900665838817386456, 54398158759680212197576, 3610650035912536155468808, 241521616482786052388206408, 16265890564063100473094045146

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..536

Formula

a(n) ~ 4480^(8/9) * 73^(n + 8/9) / (40320 * Gamma(1/9) * n^(8/9)). - Vaclav Kotesovec, Aug 18 2025

D-finite with recurrence: 2326680294400*(n + 1)*a(n) - 332099350480*(17 + 9*n)*a(n + 1) + 81980713372*(25 + 9*n)*a(n + 2) - 26736242752*(11 + 3*n)*a(n + 3) + 528962693*(41 + 9*n)*a(n + 4) - 18675041*(49 + 9*n)*a(n + 5) + 1208494*(19 + 3*n)*a(n + 6) - 5206*(65 + 9*n)*a(n + 7) + 37*(73 + 9*n)*a(n + 8) - (n + 9)*a(n + 9) = 0. - Robert Israel, Mar 13 2026

Maple

f:= gfun:-rectoproc({2326680294400*(n + 1)*a(n) - 332099350480*(17 + 9*n)*a(n + 1) + 81980713372*(25 + 9*n)*a(n + 2) - 26736242752*(11 + 3*n)*a(n + 3) + 528962693*(41 + 9*n)*a(n + 4) - 18675041*(49 + 9*n)*a(n + 5) + 1208494*(19 + 3*n)*a(n + 6) - 5206*(65 + 9*n)*a(n + 7) + 37*(73 + 9*n)*a(n + 8) - (n + 9)*a(n + 9), a(0) = 1, a(1) = 37, a(2) = 1639, a(3) = 80623, a(4) = 4257424, a(5) = 236721412, a(6) = 13688641144, a(7) = 816291120808, a(8) = 49895692924132}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Mar 13 2026

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(1/prod(k=0, 8, 1-(9*k+1)*x)^(1/9))

Crossrefs

Cf. A383627, A383628, A383629, A383630, A383631, A383633.

Sequence in context: A009695 A201956 A322097 * A260667 A130013 A370149

Adjacent sequences: A383629 A383630 A383631 * A383633 A383634 A383635

Keyword

nonn

Author

Seiichi Manyama, May 03 2025

Status

approved