OFFSET
0,2
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (12,-48,40,180,-288,-384,576,720,-320,-768,-384,-64).
FORMULA
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+5, 5)*binomial(n-k, k)*2^(n-k).
a(n) = (n+4)*(n+8)*((19*n^2 + 158*n + 275)*(n+1)*U(n+1) + 2*(7*n^2 + 52*n + 65)*(n+2)*U(n))/(2^6*3^4*5), with U(n) = A002605(n), n >= 0.
G.f.: 1/(1-2*x*(1+x))^6.
EXAMPLE
x^6 + 12*x^7 + 96*x^8 + 616*x^9 + 3444*x^10 + ... + 222249968640*x^23 + 766234140672*x^24 + 2614196680704*x^25 + 8834194123776*x^26 + ... - Zerinvary Lajos, Jun 03 2009
MATHEMATICA
CoefficientList[Series[1/(1-2*x*(1+x))^6, {x, 0, 30}], x] (* Harvey P. Dale, May 12 2018 *)
PROG
(Sage) taylor( 1/(1-2*x-2*x^2)^6, x, 0, 30).list() # Zerinvary Lajos, Jun 03 2009; modified by G. C. Greubel, Oct 04 2022
(GAP) List([0..30], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+5, 5)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x-2*x^2)^6 )); // G. C. Greubel, Oct 04 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved