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A167870
a(n) = 16^n * Sum_{k=0..n} binomial(2*k,k)^3 / 16^k.
5
1, 24, 600, 17600, 624600, 25996608, 1204834752, 59701593600, 3086972400600, 164324590337600, 8935798773354816, 494019944564058624, 27678350810730366400, 1567912312203901862400, 89647910047704725798400
OFFSET
0,2
COMMENTS
The expression a(n) = B^n*Sum_{k=0..n} binomial(2*k,k)/B^k gives A006134 for B=1, A082590 (B=2), A132310 (B=3), A002457 (B=4), A144635 (B=5), A167713 (B=16).
The expression a(n) = B^n*Sum_{k=0..n} binomial(2*k,k)^3/B^k gives A079727 for B=1, A167867 (B=2), A167868 (B=3), A167869 (B=4), A167870 (B=16), A167871 (B=64).
LINKS
FORMULA
a(n) = 16^n * Sum_{k=0..n} binomial(2*k,k)^3 / 16^k.
Recurrence: n^3*a(n) = 8*(10*n^3 - 12*n^2 + 6*n - 1)*a(n-1) - 128*(2*n-1)^3*a(n-2). - Vaclav Kotesovec, Aug 13 2013
a(n) ~ 2^(6*n+2)/(3*(Pi*n)^(3/2)). - Vaclav Kotesovec, Aug 13 2013
MATHEMATICA
Table[16^n Sum[Binomial[2k, k]^3/16^k, {k, 0, n}], {n, 0, 20}] (* Harvey P. Dale, Jan 21 2012 *)
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Nov 14 2009
EXTENSIONS
More terms from Sean A. Irvine, Apr 27 2010
STATUS
approved