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A053132 One half of binomial coefficients C(2*n-4,5). 6
3, 28, 126, 396, 1001, 2184, 4284, 7752, 13167, 21252, 32890, 49140, 71253, 100688, 139128, 188496, 250971, 329004, 425334, 543004, 685377, 856152, 1059380, 1299480, 1581255, 1909908, 2291058, 2730756, 3235501, 3812256, 4468464 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,1

COMMENTS

a(n)= A053127(n)/2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 5..200

Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

FORMULA

a(n)= binomial(2*n-4, 5)/2 if n >= 5 else 0;

G.f.: (x^5)*(3+10*x+3*x^2)/(1-x)^6.

a(n) = sum(A000217(k)*A000217(2*n-k-7): k = 1..n-4). - Reinhard Zumkeller, Mar 03 2015

MATHEMATICA

Binomial[2*Range[5, 40]-4, 5]/2 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3, 28, 126, 396, 1001, 2184}, 40] (* Harvey P. Dale, Oct 25 2015 *)

PROG

(MAGMA) [Binomial(2*n-4, 5)/2: n in [5..40]]; // Vincenzo Librandi, Oct 07 2011

(Haskell)

a053132 n = a053132_list !! (n-5)

a053132_list = f [1] $ drop 2 a000217_list where

   f xs ts'@(t:ts) = (sum $ zipWith (*) xs ts') : f (t:xs) ts

-- Reinhard Zumkeller, Mar 03 2015

CROSSREFS

Cf. A053127.

Cf. A000217.

Sequence in context: A107651 A239057 A100019 * A048367 A095665 A145346

Adjacent sequences:  A053129 A053130 A053131 * A053133 A053134 A053135

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.