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A167867 a(n) = 2^n * Sum_{k=0..n} binomial(2*k,k)^3 / 2^k. 5
1, 10, 236, 8472, 359944, 16722896, 822334816, 42068907200, 2215884717400, 119364801362800, 6545334930678816, 364137834051739200, 20502307365808906816, 1166063313963833813632, 66893439680369963627264 (list; graph; refs; listen; history; text; internal format)
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) = 2^n * Sum_{k=0..n} binomial(2*k,k)^3 / 2^k.
Recurrence: n^3*a(n) = 2*(33*n^3 - 48*n^2 + 24*n - 4)*a(n-1) - 16*(2*n-1)^3*a(n-2). - Vaclav Kotesovec, Aug 13 2013
a(n) ~ 2^(6*n+5)/(31*(Pi*n)^(3/2)). - Vaclav Kotesovec, Aug 13 2013
MATHEMATICA
Table[2^n Sum[Binomial[2k, k]^3/2^k, {k, 0, n}], {n, 0, 30}] (* Vincenzo Librandi, Mar 26 2012 *)
CROSSREFS
Sequence in context: A012240 A295410 A188679 * A268080 A096331 A159497
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Nov 14 2009
EXTENSIONS
More terms from Sean A. Irvine, Apr 27 2010
STATUS
approved

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Last modified June 18 12:25 EDT 2024. Contains 373481 sequences. (Running on oeis4.)