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A369803
Expansion of 1/(1 - x^2/(1-x)^5).
7
1, 0, 1, 5, 16, 45, 126, 361, 1046, 3032, 8771, 25348, 73252, 211724, 612009, 1769080, 5113647, 14781237, 42725841, 123501151, 356986401, 1031887518, 2982723523, 8621714049, 24921502864, 72036871920, 208226244217, 601888555723, 1739789499591, 5028950081882
OFFSET
0,4
COMMENTS
Number of compositions of 5*n-2 into parts 2 and 5.
FORMULA
a(n) = A001687(5*n-1) for n > 0.
a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5.
a(n) = Sum_{k=0..floor(n/2)} binomial(n-1+3*k,n-2*k).
a(n) = A369840(n)-A369840(n-1). - R. J. Mathar, Feb 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(1-x^2/(1-x)^5))
(PARI) a(n) = sum(k=0, n\2, binomial(n-1+3*k, n-2*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 01 2024
STATUS
approved