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a(n) = 10^n - 9^n - 8^n - 7^n + 3*6^n.
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%I #14 Sep 12 2024 19:59:49

%S 1,4,14,64,830,14704,228734,3136144,39450110,468241264,5338397054,

%T 59140070224,641540046590,6850671429424,72282030453374,

%U 755587489260304,7840735233590270,80889167950995184,830567232465613694,8495462278285810384,86620589245358801150,880864903819470714544

%N a(n) = 10^n - 9^n - 8^n - 7^n + 3*6^n.

%C Binomial transform of A081690.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (40,-635,5000,-19524,30240).

%F G.f.: -(6684*x^4-2956*x^3+489*x^2-36*x+1)/((6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)*(10*x-1)). [_Colin Barker_, Aug 12 2012]

%F From _Elmo R. Oliveira_, Sep 12 2024: (Start)

%F E.g.f.: exp(6*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).

%F a(n) = 40*a(n-1) - 635*a(n-2) + 5000*a(n-3) - 19524*a(n-4) + 30240*a(n-5) for n > 4. (End)

%Y Cf. A081690.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 30 2003

%E a(19)-a(21) from _Elmo R. Oliveira_, Sep 12 2024