Empirical: a(n) = 6*a(n-1) -16*a(n-2) +26*a(n-3) -30*a(n-4) +27*a(n-5) -21*a(n-6) +16*a(n-7) -11*a(n-8) +4*a(n-9) +4*a(n-10) -11*a(n-11) +16*a(n-12) -21*a(n-13) +27*a(n-14) -30*a(n-15) +26*a(n-16) -16*a(n-17) +6*a(n-18) -a(n-19).
Also a polynomial of degree 7 plus a degree 0 quasipolynomial with period 60; the first 12 are:
Empirical for n mod 60 = 0: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n.
Empirical for n mod 60 = 1: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (1043/60).
Empirical for n mod 60 = 2: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (462/5).
Empirical for n mod 60 = 3: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (1393/20).
Empirical for n mod 60 = 4: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (952/15).
Empirical for n mod 60 = 5: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (357/4).
Empirical for n mod 60 = 6: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (546/5).
Empirical for n mod 60 = 7: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (7931/60).
Empirical for n mod 60 = 8: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (1008/5).
Empirical for n mod 60 = 9: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n + (3129/20).
Empirical for n mod 60 = 10: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (140/3).
Empirical for n mod 60 = 11: a(n) = n^7 + (35/6)*n^6 + (91/5)*n^5 + (119/4)*n^4 + (91/3)*n^3 + (35/2)*n^2 + 6*n - (1799/20).
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