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A104473
a(n) = binomial(n+2,2)*binomial(n+6,2).
1
15, 63, 168, 360, 675, 1155, 1848, 2808, 4095, 5775, 7920, 10608, 13923, 17955, 22800, 28560, 35343, 43263, 52440, 63000, 75075, 88803, 104328, 121800, 141375, 163215, 187488, 214368, 244035, 276675, 312480, 351648, 394383, 440895, 491400, 546120, 605283, 669123
OFFSET
0,1
FORMULA
a(n) = (1/4)*(n+1)*(n+2)*(n+5)*(n+6).
a(n) = A034856(n+2)^2 - 1. - J. M. Bergot, Dec 14 2010
G.f.: -3*(x^2-4*x+5)/(x-1)^5. - Colin Barker, Sep 21 2012
a(n) = Sum_{i=1..n+1} i*(i+2)*(i+4). - Bruno Berselli, Apr 28 2014
a(n) = A000217(n)*A000217(n+4) = 3*A033275(n+4). - R. J. Mathar, Nov 29 2015
From Amiram Eldar, Aug 30 2022: (Start)
Sum_{n>=0} 1/a(n) = 43/450.
Sum_{n>=0} (-1)^n/a(n) = 16*log(2)/15 - 154/225. (End)
EXAMPLE
a(0) = C(0+2,2)*C(0+6,2) = C(2,2)*C(6,2) = 1*15 = 155.
a(10) = C(10+2,2)*C(10+6,2) = C(12,2)*(16,2) = 66*120 = 7920.
a(6) = 1*3*5 + 2*4*6 + 3*5*7 + 4*6*8 + 5*7*9 + 6*8*10 + 7*9*11 = 1848. - Bruno Berselli, Apr 28 2014
MATHEMATICA
f[n_] := Binomial[n + 2, 2] Binomial[n + 6, 2]; Table[f[n], {n, 0, 27}] (* Robert G. Wilson v, Apr 20 2005 *)
CoefficientList[Series[-3 (x^2 - 4 x + 5)/(x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 28 2014 *)
PROG
(PARI) a(n)=binomial(n+2, 2)*binomial(n+6, 2) \\ Charles R Greathouse IV, Jun 07 2013
(Magma) [Binomial(n+2, 2)*Binomial(n+6, 2): n in [0..50]]; // Vincenzo Librandi, Apr 28 2014
CROSSREFS
Subsequence of A085780.
Sequence in context: A141759 A335574 A305616 * A135972 A138104 A152099
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Apr 18 2005
STATUS
approved