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 A273889 a(n) = ((4n-3)!! + (4n-2)!!) / (4n-1). 5
 1, 9, 435, 52017, 11592315, 4152126825, 2182133628675, 1581940549814625, 1512952069890336075, 1845586177840605209625, 2796710279417971723681875, 5153962250373844341910100625, 11351091844757135191108560046875, 29444207228221006416048397134215625, 88848552445321896564985597922269171875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Hong-Chang Wang, Table of n, a(n) for n = 1..100 Brian Cheung, Proof that (4n-1) divides (4n-3)!! + (4n-2)!! Hong-Chang Wang, Bridan's blog (in Chinese) EXAMPLE a(1) = (1 + 2)/3 = 1; a(2) = (1*3*5 + 2*4*6)/7 = 9; a(3) = (1*3*5*7*9 + 2*4*6*8*10)/11 = 435. MATHEMATICA B[n_, k_] := (Product[k (i - 1) + 1, {i, 2 n - 1}] + Product[k (i - 1) + 2, {i, 2 n - 1}])/(2 k (n - 1) + 3); Table[B[n, 2], {n, 15}] (* Michael De Vlieger, Jun 10 2016 *) Table[((4n-3)!!+(4n-2)!!)/(4n-1), {n, 20}] (* Harvey P. Dale, Mar 08 2018 *) PROG (Python) for n in range(1, 101): if n == 1: a = 1 b = 2 else: a = a*(4*n-5)*(4*n-3) b = b*(4*n-4)*(4*n-2) c = (a+b)/(4*n-1) print(str(n)+" "+str(c)) CROSSREFS Cf. A000165, A001147, A006882, A004767, A103639. Sequence in context: A092813 A242280 A266294 * A167720 A287102 A173954 Adjacent sequences: A273886 A273887 A273888 * A273890 A273891 A273892 KEYWORD nonn AUTHOR Jiangshan Sun, Brian Cheung, Jason Y.S. Chiu, Hong-Chang Wang, Jun 02 2016 STATUS approved

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Last modified September 10 04:30 EDT 2024. Contains 375773 sequences. (Running on oeis4.)