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A105946
a(n) = C(n+5,n)*C(n+3,3).
1
1, 24, 210, 1120, 4410, 14112, 38808, 95040, 212355, 440440, 858858, 1589952, 2815540, 4798080, 7907040, 12651264, 19718181, 30020760, 44753170, 65456160, 94093230, 133138720, 185679000, 255528000, 347358375, 466849656, 620854794, 817586560, 1066825320
OFFSET
0,2
FORMULA
G.f.: -(10*x^3+30*x^2+15*x+1) / (x-1)^9. - Colin Barker, Jan 28 2013
From Amiram Eldar, Sep 06 2022: (Start)
Sum_{n>=0} 1/a(n) = 75*Pi^2/2 - 5905/16.
Sum_{n>=0} (-1)^n/a(n) = 160*log(2) - 5*Pi^2/4 - 4685/48. (End)
EXAMPLE
If n=0 then C(0+5,0)*C(0+3,3) = C(5,0)*C(3,3) = 1*1 = 1.
If n=15 then C(15+5,15)*C(15+3,3) = C(20,15)*C(18,3) = 15504*816 = 12651264.
MAPLE
A105946:=n->binomial(n+5, n)*binomial(n+3, 3); seq(A105946(n), n=0..100); # Wesley Ivan Hurt, Nov 26 2013
MATHEMATICA
Table[Binomial[n+5, n]*Binomial[n+3, 3], {n, 0, 100}] (* Wesley Ivan Hurt, Nov 26 2013 *)
LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {1, 24, 210, 1120, 4410, 14112, 38808, 95040, 212355}, 110] (* Harvey P. Dale, Jun 28 2015 *)
CROSSREFS
Cf. A062196.
Sequence in context: A047659 A108671 A097321 * A050222 A169635 A269496
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 27 2005
EXTENSIONS
More terms from Colin Barker, Jan 28 2013
STATUS
approved