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A004985
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a(n) = (2^n/n!)*Product_{k=0..n-1} (4*k + 5).
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1
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1, 10, 90, 780, 6630, 55692, 464100, 3845400, 31724550, 260846300, 2138939660, 17500415400, 142920059100, 1165348174200, 9489263704200, 77179344794160, 627082176452550, 5090431785320700, 41289057814267900, 334658679126171400, 2710735300921988340, 21944047674130381800
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 - 8*x)^(-5/4).
a(n) ~ 4*Gamma(1/4)^-1*n^(1/4)*2^(3*n)*{1 + 5/32*n^-1 - ...}
a(n) = 8^n*binomial(1/4 + n, 1/4).
E.g.f.: is the hypergeometric function of type 1F1, in Maple notation hypergeom([5/4], [1], 8*x). - Karol A. Penson, Dec 20 2015
D-finite with recurrence: n*a(n) +2*(-4*n-1)*a(n-1)=0. - R. J. Mathar, Jan 16 2020
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MAPLE
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a:= n-> (2^n/n!)*mul(4*k+5, k=0..n-1); seq(a(n), n=0..25); # G. C. Greubel, Aug 22 2019
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MATHEMATICA
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Table[2^n/n! Product[4k+5, {k, 0, n-1}], {n, 0, 25}] (* Harvey P. Dale, Apr 15 2019 *)
Table[8^n*Pochhammer[5/4, n]/n!, {n, 0, 25}] (* G. C. Greubel, Aug 22 2019 *)
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PROG
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(PARI) a(n)=2^n/n!*prod(k=0, n-1, 4*k+5)
for(n=0, 21, print(a(n)))
(Magma) [1] cat [2^n*&*[4*k+5: k in [0..n-1]]/Factorial(n): n in [1..25]]; // G. C. Greubel, Aug 22 2019
(Sage) [8^n*rising_factorial(5/4, n)/factorial(n) for n in (0..25)] # G. C. Greubel, Aug 22 2019
(GAP) List([0..25], n-> 2^n*Product([0..n-1], k-> 4*k+5)/Factorial(n) ); # G. C. Greubel, Aug 22 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Joe Keane (jgk(AT)jgk.org)
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EXTENSIONS
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STATUS
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approved
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