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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

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

Cf. A062264. Subsequence of A085780.

Sequence in context: A157968 A141759 A305616 * A135972 A138104 A152099

Adjacent sequences:  A104470 A104471 A104472 * A104474 A104475 A104476

KEYWORD

nonn,easy

AUTHOR

Zerinvary Lajos, Apr 18 2005

STATUS

approved

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Last modified February 18 00:28 EST 2020. Contains 332006 sequences. (Running on oeis4.)