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A103604
a(n) = C(n+6,6) * C(n+10,6).
1
210, 3234, 25872, 144144, 630630, 2312310, 7399392, 21237216, 55747692, 135795660, 310390080, 671571264, 1385115732, 2738894004, 5216940960, 9610154400, 17178150990, 29881321470, 50707697040, 84126042000, 136704818250, 217946538810, 341398774080, 526116951360
OFFSET
0,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: -42*(5*x^2+12*x+5) / (x-1)^13. - Colin Barker, Jul 01 2015
a(n) = A000579(n+6)*A000579(n+10). - Michel Marcus, Jul 01 2015
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 60*Pi^2 - 10445899/17640.
Sum_{n>=0} (-1)^n/a(n) = 447173/2205 - 2048*log(2)/7. (End)
MATHEMATICA
Table[Binomial[n+6, 6]Binomial[n+10, 6], {n, 0, 30}] (* or *) LinearRecurrence[ {13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1}, {210, 3234, 25872, 144144, 630630, 2312310, 7399392, 21237216, 55747692, 135795660, 310390080, 671571264, 1385115732}, 30] (* Harvey P. Dale, Apr 18 2019 *)
PROG
(PARI) a(n) = binomial(n+6, 6)*binomial(n+10, 6) \\ Colin Barker, Jul 01 2015
(PARI) Vec(-42*(5*x^2+12*x+5)/(x-1)^13 + O(x^30)) \\ Colin Barker, Jul 01 2015
CROSSREFS
Cf. A000579.
Sequence in context: A027822 A024449 A235240 * A257711 A061133 A087977
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Apr 22 2005
STATUS
approved