A383637 Expansion of 1/((1-x) * (1+3*x) * (1-5*x)).
1, 3, 22, 90, 511, 2373, 12412, 60420, 307021, 1520343, 7646002, 38097150, 190884331, 953225913, 4769716792, 23837822280, 119221396441, 596010127083, 2980341200782, 14900834307810, 74506786627351, 372526087871853, 1862653975153972, 9313199268385740, 46566208164081061
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (3,13,-15).
Programs
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PARI
a(n) = (5^(n+2)+(-3)^(n+2)-2)/32;
Formula
a(n) = Sum_{k=0..floor(n/2)} 16^k * binomial(n+2,2*k+2).
a(n) = (5^(n+2) + (-3)^(n+2) - 2)/32 = (A120612(n+2) - 1)/16.
a(n) = 3*a(n-1) + 13*a(n-2) - 15*a(n-3).
a(n) = Sum_{k=0..n} 4^k * (-3)^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
a(n) = Sum_{k=0..n} (-4)^k * 5^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).