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A367705
Coefficients of expansion of (1 + 5*x + 11*x^2 + 5*x^3 + 7*x^4 + x^5)/(1 - x^3)^2 in powers of x.
0
1, 5, 11, 7, 17, 23, 13, 29, 35, 19, 41, 47, 25, 53, 59, 31, 65, 71, 37, 77, 83, 43, 89, 95, 49, 101, 107, 55, 113, 119, 61, 125, 131, 67, 137, 143, 73, 149, 155, 79, 161, 167, 85, 173, 179, 91, 185, 191, 97, 197, 203, 103, 209, 215, 109, 221, 227, 115, 233, 239
OFFSET
0,2
COMMENTS
Based on an idea of Pierre CAMI.
FORMULA
a(n) = 3*A006369(n) + A130196(n).
a(n) = A007310(A006369(n) + 1).
a(n) = 2*a(n-3) - a(n-6) for n >= 6.
a(3*n) = 6*n+1, a(3*n+1) = 12*n+5, a(3*n+2) = 12*n+11.
Sum_{n>=0} (-1)^n/a(n) = ((2+sqrt(2))*Pi + sqrt(3)*log(7+4*sqrt(3)) + sqrt(6)*log(5-2*sqrt(6)))/12. - Amiram Eldar, Nov 28 2023
MATHEMATICA
CoefficientList[Series[(1 + 5*x + 11*x^2 + 5*x^3 + 7*x^4 + x^5)/(1 - x^3)^2, {x, 0, 60}], x] (* or *)
LinearRecurrence[{0, 0, 2, 0, 0, -1}, {1, 5, 11, 7, 17, 23}, 60] (* Amiram Eldar, Nov 28 2023 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Nov 27 2023
STATUS
approved