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A093567 Binomial (Binomial (n,2), 3) - Binomial (Binomial (n,3), 2). 1
0, 1, 14, 75, 265, 735, 1736, 3654, 7050, 12705, 21670, 35321, 55419, 84175, 124320, 179180, 252756, 349809, 475950, 637735, 842765, 1099791, 1418824, 1811250, 2289950, 2869425, 3565926, 4397589, 5384575, 6549215, 7916160, 9512536 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,3

COMMENTS

All terms are positive: A093566 >= A054563 ==> C( C(n,2), 3) >= C( C(n,3), 2) ==> n^2*(n^4 + 3n^3 -35n^2 + 69n -38)/144 >= 0 ==> (n - 2)(n - 1)(n^2 + 6n - 19) ==> 0 which it is for all n >= 2.

LINKS

Table of n, a(n) for n=2..33.

Solomon W. Golomb, Iterated binomial coefficients, Amer. Math. Monthly, 87 (1980), 719-727.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = A093566(n) - A054563(n).

G.f.:  x^3*(-1-7*x+2*x^2+x^3)/(x-1)^7. - R. J. Mathar, Dec 08 2010

MAPLE

A093567:=n->binomial(binomial(n, 2), 3) - binomial(binomial(n, 3), 2); seq(A093567(n), n=2..30); # Wesley Ivan Hurt, Feb 02 2014

MATHEMATICA

Table[ Binomial[ Binomial[n, 2], 3] - Binomial[ Binomial[n, 3], 2], {n, 2, 34}]

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 1, 14, 75, 265, 735, 1736}, 40] (* Harvey P. Dale, Jun 12 2016 *)

PROG

(PARI) a(n) = binomial(binomial(n, 2), 3) - binomial(binomial(n, 3), 2); \\ Michel Marcus, Oct 01 2017

CROSSREFS

Cf. A054563, A093566.

Sequence in context: A167633 A196411 A108650 * A296996 A270704 A200554

Adjacent sequences:  A093564 A093565 A093566 * A093568 A093569 A093570

KEYWORD

nonn

AUTHOR

Robert G. Wilson v and Santi Spadaro, Mar 31 2004

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)