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A016817
a(n) = (4n+1)^5.
1
1, 3125, 59049, 371293, 1419857, 4084101, 9765625, 20511149, 39135393, 69343957, 115856201, 184528125, 282475249, 418195493, 601692057, 844596301, 1160290625, 1564031349, 2073071593, 2706784157, 3486784401, 4437053125, 5584059449, 6956883693, 8587340257, 10510100501
OFFSET
0,2
FORMULA
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Wesley Ivan Hurt, Apr 12 2023
From Amiram Eldar, Apr 21 2023: (Start)
a(n) = A016813(n)^5.
Sum_{n>=0} 1/a(n) = 5*Pi^5/3072 + 31*zeta(5)/64. (End)
MATHEMATICA
Table[(4n+1)^5, {n, 0, 100}] (* Mohammad K. Azarian, Jun 18 2016 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 3125, 59049, 371293, 1419857, 4084101}, 30] (* Harvey P. Dale, Oct 02 2022 *)
CROSSREFS
Sequence in context: A223184 A084649 A169754 * A115791 A016853 A016973
KEYWORD
nonn,easy
STATUS
approved