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 (6,-3,-40,45,126,-141,-252,180,320,-48,-192,-64).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+5, 5) * binomial(n-k, k) * 2^k.
a(n) = (n+3)*(n+9)*((3080 +1086*n +93*n^2)*(n+1)*U(n+1) + 2*(1660 +591*n +51*n^2) *(n+2)*U(n))/(5!*3^7) with U(n) = A001045(n+1), n>=0.
G.f.: 1/(1-(1+2*x)*x)^6 = 1/((1+x)*(1-2*x))^6.
E.g.f.: (1/787320)*(1024*(675 +3470*x +4195*x^2 +1830*x^3 +315*x^4 +18*x^5 )*exp(2*x) + (96120 -115640*x +42440*x^2 -6360*x^3 +405*x^4 -9*x^5)*exp(-x)). - G. C. Greubel, Sep 29 2022
MATHEMATICA
Table[(n+3)*(n+9)*(2^(6+n)*(9*n^3 +117*n^2 +438*n +400) +(-1)^n*(9*n^3 +207*n^2 + 1518*n +3560))/787320, {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)
PROG
(Magma) [(n+3)*(n+9)*(2^(6+n)*(9*n^3 +117*n^2 +438*n +400) +(-1)^n*(9*n^3 +207*n^2 + 1518*n +3560))/787320: n in [0..40]]; // G. C. Greubel, Sep 29 2022
(SageMath)
def A073375(n): return (n+3)*(n+9)*(2^(6+n)*(9*n^3 +117*n^2 +438*n +400) +(-1)^n*(9*n^3 +207*n^2 + 1518*n +3560))/787320
[A073375(n) for n in range(40)] # G. C. Greubel, Sep 29 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved