login
A107418
a(n) = C(n+3,3)*C(n+6,6).
1
1, 28, 280, 1680, 7350, 25872, 77616, 205920, 495495, 1101100, 2290288, 4504864, 8446620, 15193920, 26356800, 44279424, 72299997, 115079580, 179012680, 272734000, 407737330, 599124240, 866502000, 1235052000, 1736791875, 2412056556, 3311225568, 4496726080, 6045343480
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: (20*x^3+45*x^2+18*x+1)/(x-1)^10. - Robert Israel, Feb 24 2017
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 63*Pi^2 - 124149/200.
Sum_{n>=0} (-1)^n/a(n) = 3*Pi^2/2 + 1344*log(2)/5 - 40031/200. (End)
EXAMPLE
If n=0 then C(0+3,3)*C(0+6,6) = C(3,3)*C(6,6) = 1*1 = 1.
If n=8 then C(8+3,3)*C(8+6,6) = C(11,3)*C(14,6) = 165*3003 = 495495.
MAPLE
seq(binomial(n+3, 3)*binomial(n+6, 6), n=0..100); # Robert Israel, Feb 24 2017
MATHEMATICA
a[n_] := Binomial[n + 3, 3] * Binomial[n + 6, 6]; Array[a, 30, 0] (* Amiram Eldar, Sep 06 2022 *)
PROG
(PARI) for(n=0, 29, print1(binomial(n+3, 3)*binomial(n+6, 6), ", "))
CROSSREFS
Cf. A062145.
Sequence in context: A126549 A300297 A250649 * A183484 A241621 A027781
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, May 26 2005
EXTENSIONS
Corrected and extended by Rick L. Shepherd, May 27 2005
STATUS
approved