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A103639
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a(n) = Product_{i=1..2n} 2*i+1.
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6
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1, 15, 945, 135135, 34459425, 13749310575, 7905853580625, 6190283353629375, 6332659870762850625, 8200794532637891559375, 13113070457687988603440625, 25373791335626257947657609375, 58435841445947272053455474390625, 157952079428395476360490147277859375
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..13.
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FORMULA
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a(n) = (4n+2)! / [2 * 4^n * (2n+1)! ].
E.g.f.: sinh(x^2/2) = x^2/2! + 15x^6/6! + 945x^10/10! +...
Recurrence: a(n+1) = (4n-1)(4n+1)*a(n), a(0) = 1.
a(n) = (4n+1)!!. - Vladimir Reshetnikov, Nov 03 2015
a(n) = denominator((-3/2 - 2*n)!/sqrt(Pi)). - Peter Luschny, Jun 21 2020
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EXAMPLE
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Sequence starts 1, 1*3*5, 1*3*5*7*9, 1*3*5*7*9*11*13, ...
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MAPLE
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A103639 := n -> pochhammer(1/2, 2*n+1)*2^(2*n+1):
seq(A103639(n), n=0..11); # Peter Luschny, Dec 19 2012
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MATHEMATICA
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Table[(4n+1)!!, {n, 0, 15}] (* Vladimir Reshetnikov, Nov 03 2015 *)
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PROG
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(Sage)
def A103639(n):
return falling_factorial(4*n+2, 2*n+1)*2^(-1-2*n)
print([A103639(n) for n in (0..11)]) # Peter Luschny, Dec 14 2012
(PARI) vector(20, n, n--; prod(i=1, 2*n, 2*i+1)) \\ Altug Alkan, Nov 04 2015
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CROSSREFS
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Bisection of the double factorials A001147. Cf. A102992.
Cf. Odd part of A024343 and A009564.
Sequence in context: A261067 A136419 A231121 * A055413 A067408 A274713
Adjacent sequences: A103636 A103637 A103638 * A103640 A103641 A103642
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Feb 18 2005
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STATUS
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approved
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