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A103870
a(n) = Sum_{k=0..n} binomial(2*n,k)*binomial(n,k)*binomial(2*k,n).
0
1, 4, 44, 580, 8428, 129504, 2063996, 33752576, 562597100, 9516705808, 162878088544, 2814359798936, 49015445212156, 859377160206400, 15153426645082560, 268521098568718080, 4778754834452368620, 85368326032573042800, 1530167828649835039280, 27509703980465935998896
OFFSET
0,2
FORMULA
Recurrence: 3*n^2*(3*n-2)*(3*n-1)*(77*n^2 - 209*n + 142)*a(n) = (37345*n^6 - 176055*n^5 + 326171*n^4 - 302717*n^3 + 148556*n^2 - 36660*n + 3600)*a(n-1) + 128*(n-1)^2*(2*n-3)^2*(77*n^2 - 55*n + 10)*a(n-2). - Vaclav Kotesovec, Mar 02 2014
a(n) ~ 4 * (512/27)^n / (sqrt(21)*Pi*n). - Vaclav Kotesovec, Mar 02 2014
MATHEMATICA
Table[Sum[Binomial[2*n, k]*Binomial[n, k]*Binomial[2*k, n], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *)
CROSSREFS
Sequence in context: A222288 A053315 A005721 * A371680 A056063 A218224
KEYWORD
nonn
AUTHOR
Detlef Pauly (dettodet(AT)yahoo.de), Nov 08 2001
EXTENSIONS
Edited by N. J. A. Sloane, Aug 31 2008 at the suggestion of Jeffrey Shallit
Name edited by Michel Marcus, Jan 31 2023
STATUS
approved