OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).
FORMULA
a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3) + 192 for n > 3.
a(n) = Sum_{k=0..4} (-1)^k * k! * binomial(4,k) * Stirling2(n,k).
a(n) = Sum_{k=0..4} (-1)^k * 2^(4-k) * binomial(4,k) * k^n.
G.f.: (1-14*x+83*x^2-262*x^3+384*x^4)/((1-x) * (1-2*x) * (1-3*x) * (1-4*x)).
a(n) = 4^n - 8*3^n + 3*2^(n+3) - 32 for n > 0. - Stefano Spezia, Oct 27 2024
a(0) = 1; a(n) = Sum_{k=1..n} (1 - 5 * k/n) * binomial(n,k) * a(n-k). - Seiichi Manyama, Oct 27 2024
PROG
(PARI) a(n) = sum(k=0, 4, (-1)^k*k!*binomial(4, k)*stirling(n, k, 2));
(PARI) a(n) = sum(k=0, 4, (-1)^k*2^(4-k)*binomial(4, k)*k^n);
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Seiichi Manyama, Oct 27 2024
STATUS
approved