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 (5,0,-30,15,81,-30,-120,0,80,32).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+4, 4) * binomial(n-k, k) * 2^k.
a(n) = (5*(2968 +1974*n +411*n^2 +27*n^3)*(n+1)*U(n+1) + 2*(9412 +6099*n +1248*n^2 +81*n^3)*(n+2)*U(n))/(4!*3^7) with U(n) = A001045(n+1), n>=0.
G.f.: 1/(1-(1+2*x)*x)^5 = 1/((1+x)*(1-2*x))^5.
E.g.f.: (1/157464)*(512*(263 + 1104*x + 1026*x^2 + 306*x^3 + 27*x^4)*exp(2*x) + (22808 - 24432*x + 7344*x^2 - 792*x^3 + 27*x^4)*exp(-x)). - G. C. Greubel, Sep 29 2022
MATHEMATICA
Table[(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464, {n, 0, 40}] (* G. C. Greubel, Sep 29 2022 *)
PROG
(Magma) [(2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464: n in [0..40]]; // G. C. Greubel, Sep 29 2022
(SageMath)
def A073374(n): return (2^(n+5)*(4208+5790*n+2565*n^2+450*n^3+27*n^4) + (-1)^n*(22808+18510*n+ 5265*n^2+630*n^3+27*n^4))/157464
[A073374(n) for n in range(40)] # G. C. Greubel, Sep 29 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved