OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-12,-56,154,168,-700,-328,1791,656,-2800,-1344, 2464,1792,-768,-1024,-256).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+7, 7) * binomial(n-k, k) * 2^k.
a(n) = ((328247920 +332102604*n +131833680*n^2 +26450901*n^3 +2844099*n^4 + 156087*n^5 +3429*n^6)*(n+1)*U(n+1) + 2(141143240 +150941694*n +62335731*n^2 + 12873492*n^3 +1414314*n^4 +78894*n^5 +1755*n^6)*(n+2)*U(n))/(7!*3^11) with U(n) = A001045(n+1), n>=0.
G.f.: 1/(1-(1+2*x)*x)^8 = 1/((1+x)*(1-2*x))^8.
E.g.f.: (1/(7!*3^12))*( 4096*(596225 +4177950*x +7304850*x^2 +5109300*x^3 +1691550*x^4 +278964*x^5 +21924*x^6 +648*x^7)*exp(2*x) + (236325040 -333132240*x +158026680*x^2 -34637400*x^3 +3921750*x^4 -234738*x^5 +6993*x^6 -81*x^7)*exp(-x) ). - G. C. Greubel, Sep 29 2022
MATHEMATICA
Table[(2^(n+8)*(9539600 +17240268*n +11555460*n^2 +3849489*n^3 +703080*n^4 +71442*n^5 +3780*n^6 +81*n^7) +(-1)^n*(236325040 +225702732*n +87290028*n^2 +17880849*n^3 +2109240*n^4 +144018*n^5 +5292*n^6 +81*n^7))/(7!*3^12), {n, 0, 60}] (* G. C. Greubel, Sep 29 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/((1+x)*(1-2*x))^8 )); // G. C. Greubel, Sep 29 2022
(SageMath)
def A073377(n): return (2^(n+8)*(9539600 +17240268*n +11555460*n^2 +3849489*n^3 +703080*n^4 +71442*n^5 +3780*n^6 +81*n^7) +(-1)^n*(236325040 +225702732*n +87290028*n^2 +17880849*n^3 +2109240*n^4 +144018*n^5 +5292*n^6 +81*n^7))/(factorial(7)*3^12)
[A073377(n) for n in range(40)] # G. C. Greubel, Sep 29 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved