OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (120,-5135,105130,-1138875,6873212,-23367945,44115210,-45855180,24607800,-5334336).
FORMULA
a(n) = 56^n - (5*n + 1)*21^n + binomial(5*n+1, 2)*6^n - binomial(5*n+1, 3). - Andrew Howroyd, May 07 2020
From G. C. Greubel, Sep 12 2022: (Start)
a(n) = Sum_{j=0..3} (-1)^j*binomial(5*n+1, j)*binomial(8-j, 5)^n.
G.f.: 25*x^2*(4 + 1632*x + 7949*x^2 - 594490*x^3 + 1502565*x^4 + 3945816*x^5 - 13945932*x^6 - 4667544*x^7)/( Product_{j=0.3} (1 - binomial(j+5, 5)*x)^(4-j) ).
E.g.f.: exp(56*x) - (1 + 105*x)*exp(21*x) + 90*x*(1 + 5*x)*exp(6*x) - (5/6)*x*(24 + 75*x + 25*x^2)*exp(x). (End)
MATHEMATICA
Table[Sum[(-1)^j*Binomial[5*n+1, j]*Binomial[8-j, 5]^n, {j, 0, 3}], {n, 30}] (* G. C. Greubel, Sep 12 2022 *)
PROG
(PARI) a(n) = {56^n - (5*n + 1)*21^n + binomial(5*n+1, 2)*6^n - binomial(5*n+1, 3)} \\ Andrew Howroyd, May 07 2020
(Magma) [(&+[(-1)^j*Binomial(5*n+1, j)*Binomial(8-j, 5)^n: j in [0..3]]): n in [1..30]]; // G. C. Greubel, Sep 12 2022
(SageMath)
def A151648(n): return sum((-1)^j*binomial(5*n+1, j)*binomial(8-j, 5)^n for j in (0..3))
[A151648(n) for n in (1..30)] # G. C. Greubel, Sep 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, May 29 2009
EXTENSIONS
Terms a(8) and beyond from Andrew Howroyd, May 07 2020
STATUS
approved