OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..670
FORMULA
a(n) ~ 31^(n + 15/16) / (Gamma(1/16) * 2^(41/16) * 3^(3/8) * 5^(3/16) * 7^(1/8) * 143^(1/16) * n^(15/16)). - Vaclav Kotesovec, May 12 2025
D-finite with recurrence: 191898783962510625*(n + 1)*a(n) + 9232590499695675*(31 + 16*n)*a(n + 1) - 7502121379090845*(23 + 8*n)*a(n + 2) - 837506736967419*(61 + 16*n)*a(n + 3) + 700477720652271*(19 + 4*n)*a(n + 4) + 19993782640195*(91 + 16*n)*a(n + 5) - 5739184340435*(53 + 8*n)*a(n + 6) - 193883452763*(121 + 16*n)*a(n + 7) + 171951015379*(17 + 2*n)*a(n + 8) + 898253785*(151 + 16*n)*a(n + 9) - 164130395*(83 + 8*n)*a(n + 10) - 2091817*(181 + 16*n)*a(n + 11) + 656383*(49 + 4*n)*a(n + 12) + 2345*(211 + 16*n)*a(n + 13) - 325*(113 + 8*n)*a(n + 14) - (241 + 16*n)*a(n + 15) + (n + 16)*a(n + 16) = 0. - Robert Israel, Mar 12 2026
MAPLE
f:= gfun:-rectoproc({191898783962510625*(n + 1)*a(n) + 9232590499695675*(31 + 16*n)*a(n + 1) - 7502121379090845*(23 + 8*n)*a(n + 2) - 837506736967419*(61 + 16*n)*a(n + 3) + 700477720652271*(19 + 4*n)*a(n + 4) + 19993782640195*(91 + 16*n)*a(n + 5) - 5739184340435*(53 + 8*n)*a(n + 6) - 193883452763*(121 + 16*n)*a(n + 7) + 171951015379*(17 + 2*n)*a(n + 8) + 898253785*(151 + 16*n)*a(n + 9) - 164130395*(83 + 8*n)*a(n + 10) - 2091817*(181 + 16*n)*a(n + 11) + 656383*(49 + 4*n)*a(n + 12) + 2345*(211 + 16*n)*a(n + 13) - 325*(113 + 8*n)*a(n + 14) - (241 + 16*n)*a(n + 15) + (n + 16)*a(n + 16), a(0) = 1, a(1) = 1, a(2) = 171, a(3) = 511, a(4) = 67219, a(5) = 332691, a(6) = 35484101, a(7) = 243740561, a(8) = 21888901107, a(9) = 191172628003, a(10) = 14869055610001, a(11) = 156592613526141, a(12) = 10782221986043741, a(13) = 132098336706362573, a(14) = 8194613483517245067, a(15) = 113784873403069510831}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Mar 12 2026
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(1/prod(k=0, 15, 1+(-1)^k*(2*k+1)*x)^(1/16))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 03 2025
STATUS
approved