editing

approved

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 13 2004

Wolfdieter Lang, Feb 13 2004

approved

editing

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).

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

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.

nonn,easy,new

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. ref. reference given in A078740 with r=6,s=2,k=3.

nonn,easy,new

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

0,2,2

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. ref. given in A007840 with r=6,s=2,k=3.

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. ref. given in A078740 with r=6,s=2,k=3.

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

nonn,easy,new

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

1, 160, 39900, 15120000, 8202070800, 6058891238400, 5860547004312000, 7196668193594880000, 10944624305020966560000, 20199809308312018344960000, 44490168120726255724917120000, 115290834599202214240544256000000

0,2

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. ref. given in A007840 with r=6,s=2,k=3.

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).

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

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

nonn,easy,new

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 13 2004

approved