# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a004985 Showing 1-1 of 1 %I A004985 #32 Sep 08 2022 08:44:33 %S A004985 1,10,90,780,6630,55692,464100,3845400,31724550,260846300,2138939660, %T A004985 17500415400,142920059100,1165348174200,9489263704200,77179344794160, %U A004985 627082176452550,5090431785320700,41289057814267900,334658679126171400,2710735300921988340,21944047674130381800 %N A004985 a(n) = (2^n/n!)*Product_{k=0..n-1} (4*k + 5). %H A004985 G. C. Greubel, Table of n, a(n) for n = 0..1000 %F A004985 G.f.: (1 - 8*x)^(-5/4). %F A004985 a(n) ~ 4*Gamma(1/4)^-1*n^(1/4)*2^(3*n)*{1 + 5/32*n^-1 - ...} %F A004985 a(n) = 8^n*binomial(1/4 + n, 1/4). %F A004985 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 %F A004985 D-finite with recurrence: n*a(n) +2*(-4*n-1)*a(n-1)=0. - _R. J. Mathar_, Jan 16 2020 %p A004985 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 %t A004985 Table[2^n/n! Product[4k+5,{k,0,n-1}],{n,0,25}] (* _Harvey P. Dale_, Apr 15 2019 *) %t A004985 Table[8^n*Pochhammer[5/4, n]/n!, {n,0,25}] (* _G. C. Greubel_, Aug 22 2019 *) %o A004985 (PARI) a(n)=2^n/n!*prod(k=0,n-1,4*k+5) %o A004985 for(n=0,21,print(a(n))) %o A004985 (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 %o A004985 (Sage) [8^n*rising_factorial(5/4, n)/factorial(n) for n in (0..25)] # _G. C. Greubel_, Aug 22 2019 %o A004985 (GAP) List([0..25], n-> 2^n*Product([0..n-1], k-> 4*k+5)/Factorial(n) ); # _G. C. Greubel_, Aug 22 2019 %K A004985 nonn,easy %O A004985 0,2 %A A004985 Joe Keane (jgk(AT)jgk.org) %E A004985 More terms from _Rick L. Shepherd_, Mar 03 2002 %E A004985 Terms a(20) onward added by _G. C. Greubel_, Aug 22 2019 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE