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 A091550 Second column (k=3) sequence of array A091746 ((6,2)-Stirling2) divided by 12. 3

%I #6 Sep 30 2012 07:29:24

%S 1,160,39900,15120000,8202070800,6058891238400,5860547004312000,

%T 7196668193594880000,10944624305020966560000,

%U 20199809308312018344960000,44490168120726255724917120000,115290834599202214240544256000000

%N Second column (k=3) sequence of array A091746 ((6,2)-Stirling2) divided by 12.

%F a(n)=(2^(4*n))*risefac(1/2, n)*(-3*risefac(1/4, n) + risefac(3/4, n))/(3!*12), n>=2, with risefac(x, n)=Pochhammer(x, n).

%F E.g.f.: (hypergeom([1/2, 3/4], [], 16*x) - 3*hypergeom([1/4, 1/2], [], 16*x) + 2)/(3!*12).

%F a(n)=(2^n)*product(2*j+1, j=0..n-1)* (-3*product(4*j+1, j=0..n-1) + product(4*j+3, j=0..n-1))/(3!*12), n>=2. From eq.12 of the Blasiak et al. reference given in A078740 with r=6, s=2, k=3.

%Y Cf. A091539 (second column of (5, 2)-Stirling2 array), A091550 (second column of (7, 2)-Stirling2 array).

%K nonn,easy

%O 2,2

%A _Wolfdieter Lang_, Feb 13 2004

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Last modified August 9 11:18 EDT 2024. Contains 375041 sequences. (Running on oeis4.)