A383628 Expansion of 1/( Product_{k=0..3} (1 - (4*k+1) * x) )^(1/4).

1, 7, 59, 553, 5555, 58597, 640789, 7201383, 82659891, 964698805, 11408855809, 136374495803, 1644405320701, 19971195162107, 244004256374395, 2996243293813273, 36950056359522771, 457349452121086917, 5678884294812093329, 70710759962448700955, 882616583068179751945

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..896

Formula

a(n) ~ 13^(n + 3/4) / (Gamma(1/4) * 2^(7/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Aug 18 2025

D-finite with recurrence: (585 + 585*n)*a(n) + (-1421 - 812*n)*a(n + 1) + (635 + 254*n)*a(n + 2) + (-91 - 28*n)*a(n + 3) + (n + 4)*a(n + 4) = 0. - Robert Israel, Mar 13 2026

Maple

f:= gfun:-rectoproc({(585 + 585*n)*a(n) + (-1421 - 812*n)*a(n + 1) + (635 + 254*n)*a(n + 2) + (-91 - 28*n)*a(n + 3) + (n + 4)*a(n + 4), a(0) = 1, a(1) = 7, a(2) = 59, a(3) = 553}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Mar 13 2026

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(1/prod(k=0, 3, 1-(4*k+1)*x)^(1/4))

Crossrefs

Cf. A383627, A383629, A383630, A383631, A383632, A383633.

Cf. A383634.

Sequence in context: A363105 A101487 A210397 * A099659 A358599 A135150

Adjacent sequences: A383625 A383626 A383627 * A383629 A383630 A383631

Keyword

nonn

Author

Seiichi Manyama, May 03 2025

Status

approved