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a(n) = 1/([x^n] hypergeom([1], [1], x/2)). - Peter Luschny, Sep 13 2024
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The sequence b(n) = A068102(n) also satisfies this second-order recurrence. This leads to the generalized continued fraction expansion lim_{n -> infinityoo} b(n)/a(n) = log(2) = 1/(2 - 2/(5 - 8/(8 - 18/(11 - ... - 2*(n - 1)^2/((3*n - 1) - ... ))))). (End)
Limit_{n->infinityoo} a(n)^4 / (n * A134372(n)) = Pi. - Daniel Suteu, Apr 09 2022
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exp(x/2) =sum( Sum_{n>=0,} x^n/a(n)). - Jaume Oliver Lafont, Sep 07 2009
Table[(2 n)!!, {n, 2030}] (* Vladimir Joseph Stephan Orlovsky, Dec 13 2008 *)
(2 Range[0, 2030])!! (* Harvey P. Dale, Jan 23 2015 *)
RecurrenceTable[{a[n] == 2 n*a[n - 1], a[0] == 1}, a, {n, 0, 1930}] (* Ray Chandler, Jul 30 2015 *)
(Magma) [2^n*Factorial(n): n in [0..10535]]; // Vincenzo Librandi, Apr 22 2011
(Magma) I:=[2, 8]; [1] cat [n le 2 select I[n] else (3*n-1)*Self(n-1)-2*(n-1)^2*Self(n-2): n in [1..2535] ]; // Vincenzo Librandi, Feb 19 2015
(SageMath) [2^n*factorial(n) for n in range(31)] # G. C. Greubel, Jul 21 2024
Cf. A006882, A000142 (n!), A001147 ((2n-1)!!), A010050, A002454, A039683, A008544, A001813, A047053, A047055, A047058, A047657, A084947, A084948, A084949, A028326, A193229, A208057, A032184 (2^n*(n-1)!), A019774, A092605.
Cf. A000079, A000108, A000111, A001044, A001563, A001804, A001805, A001806.
Cf. A001807, A001813, A001907, A002454, A006882, A007060, A008277, A008544.
Cf. A010050, A019774, A028326, A028338, A035038, A039683, A047053, A047055.
Cf. A047058, A047657, A075271, A084947, A084948, A084949, A092605, A133314.
Cf. A145271, A193229, A208057.
This sequence gives the row sums in A060187, and (-1)^n*a(n) the alternating row sums in A039757. Also row sums in A028338.
Also row sums in A028338.
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