OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=9) of 5 objects: u, v, z, x, y with repetition allowed, containing exactly nine (9) u's. - Zerinvary Lajos, Jul 02 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (40,-720,7680,-53760,258048,-860160,1966080,-2949120,2621440,-1048576).
FORMULA
a(n) = binomial(n+9, 9)*4^n.
G.f.: 1/(1 - 4*x)^10.
a(n) = A054335(n+19, 19).
E.g.f.: (2^7/9!)*(2835 + 102060*x + 816480*x^2 + 2540160*x^3 + 3810240*x^4 + 3048192*x^5 + 1354752*x^6 + 331776*x^7 + 41472*x^8 + 2048*x^9)*exp(4*x).
From Amiram Eldar, Mar 27 2022: (Start)
Sum_{n>=0} 1/a(n) = 236196*log(4/3) - 4756383/70.
Sum_{n>=0} (-1)^n/a(n) = 14062500*log(5/4) - 43931373/14. (End)
MAPLE
seq(binomial(n+9, 9)*4^n, n=0..20); # Zerinvary Lajos, Jul 02 2008
MATHEMATICA
Table[4^n*Binomial[n+9, 9], {n, 0, 20}] (* G. C. Greubel, Jul 21 2019 *)
PROG
(Magma) [4^n*Binomial(n+9, 9): n in [0..20]]; // Vincenzo Librandi, Oct 15 2011
(PARI) vector(20, n, n--; 4^n*binomial(n+9, 9)) \\ G. C. Greubel, Jul 21 2019
(GAP) List([0..20], n-> 4^n*Binomial(n+9, 9)); # G. C. Greubel, Jul 21 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Wolfdieter Lang, Mar 13 2000
STATUS
approved