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A105254
a(n) = binomial(n+7,n)*binomial(n+11,n).
0
1, 96, 2808, 43680, 450450, 3459456, 21237216, 109219968, 486370170, 1921462400, 6859620768, 22449667968, 68128506264, 193501082880, 518306472000, 1317650231040, 3196331224515, 7432299594720, 16630917303000, 35933837940000, 75191555889450, 152770145299200
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (19,-171,969,-3876,11628,-27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876,-969,171,-19,1).
FORMULA
G.f.: -(330*x^7+3234*x^6+9702*x^5+11550*x^4+5775*x^3+1155*x^2+77*x+1)/(x-1)^19. - Colin Barker, Jan 21 2013
From Amiram Eldar, Sep 04 2022: (Start)
Sum_{n>=0} 1/a(n) = 308308*Pi^2/3 - 16431524791/16200.
Sum_{n>=0} (-1)^n/a(n) = 1232*Pi^2/3 + 360448*log(2)/45 - 108911693/11340. (End)
EXAMPLE
a(0): C(0+7,0)*C(0+11,0) = C(7,0)*C(11,0) = 1*1 = 1;
a(8): C(8+7,8)*C(8+11,8) = C(15,8)*(19,8) = 6435*75582 = 486370170.
MATHEMATICA
f[n_] := Binomial[n + 7, n]Binomial[n + 11, n]; Table[ f[n], {n, 0, 19}] (* Robert G. Wilson v, Apr 20 2005 *)
PROG
(Magma) [Binomial(n+7, n)*Binomial(n+11, n): n in [0..30]]; // Vincenzo Librandi, Jul 31 2015
CROSSREFS
Sequence in context: A233709 A268901 A239158 * A234075 A347753 A164762
KEYWORD
easy,nonn
AUTHOR
Zerinvary Lajos, Apr 14 2005
EXTENSIONS
More terms from Robert G. Wilson v, Apr 20 2005
More terms from Colin Barker, Jan 21 2013
STATUS
approved