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Empirical: a(n) = 5*a(n-1) -11*a(n-2) +15*a(n-3) -15*a(n-4) +12*a(n-5) -9*a(n-6) +7*a(n-7) -4*a(n-8) +4*a(n-10) -7*a(n-11) +9*a(n-12) -12*a(n-13) +15*a(n-14) -15*a(n-15) +11*a(n-16) -5*a(n-17) +a(n-18)
Also a polynomial of degree 6 plus a quasipolynomial of degree 0 with period 60, the first 12 being:
Empirical for n mod 60 = 0: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + 1
Empirical for n mod 60 = 1: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (983/60)
Empirical for n mod 60 = 2: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (467/5)
Empirical for n mod 60 = 3: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (1373/20)
Empirical for n mod 60 = 4: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (967/15)
Empirical for n mod 60 = 5: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (353/4)
Empirical for n mod 60 = 6: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (551/5)
Empirical for n mod 60 = 7: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (7871/60)
Empirical for n mod 60 = 8: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (1013/5)
Empirical for n mod 60 = 9: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n - (3109/20)
Empirical for n mod 60 = 10: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (143/3)
Empirical for n mod 60 = 11: a(n) = (7/6)*n^6 + (14/5)*n^5 + (21/4)*n^4 + (14/3)*n^3 + (7/2)*n^2 + n + (1819/20)
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