A093567 - OEIS

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A093567

Binomial (Binomial (n,2), 3) - Binomial (Binomial (n,3), 2).

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

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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