OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (35, -511, 4099, -19997, 61981, -123645, 157041, -122094, 52812, -9720).
FORMULA
a(n) = 10^n - (2*n + 1)*6^n + binomial(2*n+1, 2)*3^n - binomial(2*n+1, 3). - Andrew Howroyd, May 07 2020
From G. C. Greubel, Sep 07 2022: (Start)
G.f.: 4*x^3*(5 + 117*x - 749*x^2 - 831*x^3 + 6768*x^4 - 5022*x^5 - 3888*x^6)/((1-x)^4*(1-3*x)^3*(1-6*x)^2*(1-10*x)).
E.g.f.: exp(10*x) - (1+12*x)*exp(6*x) + 9*x*(1+2*x)*exp(3*x) - x*(3 + 12*x + 4*x^2)*exp(x)/3. (End)
MATHEMATICA
With[{B=Binomial}, Table[Sum[(-1)^j*B[2n+1, 4-j]*B[j+1, 2]^n, {j, 4}], {n, 30}]] (* G. C. Greubel, Sep 07 2022 *)
PROG
(PARI) a(n) = {10^n - (2*n + 1)*6^n + binomial(2*n+1, 2)*3^n - binomial(2*n+1, 3)} \\ Andrew Howroyd, May 07 2020
(Magma)
A151625:= func< n | (&+[(-1)^j*Binomial(2*n+1, 4-j)*Binomial(j+1, 2)^n: j in [1..4]]) >;
[A151625(n): n in [1..30]]; // G. C. Greubel, Sep 07 2022
(SageMath)
@CachedFunction
def A151625(n): return sum((-1)^j*binomial(2*n+1, 4-j)*binomial(j+1, 2)^n for j in (1..4))
[A151625(n) for n in (1..30)] # G. C. Greubel, Sep 07 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 29 2009
EXTENSIONS
Terms a(12) and beyond from Andrew Howroyd, May 07 2020
STATUS
approved