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A172018
a(n) = A142458(2*n-1, n)/n.
1
1, 4, 182, 27410, 8890310, 5051270688, 4459786293372, 5659222645997646, 9770821427711370950, 22041005972637205198568, 62967534725721252354766676, 222256499446324679350316816644, 950020052553444052606973276792092, 4836606673194788521307702032786510240, 28920975283745982162014025622769293094712
OFFSET
1,2
LINKS
FORMULA
a(n) = A142458(2*n-1, n)/n.
MATHEMATICA
T[n_, k_, m_]:= T[n, k, m]= If[k==1 || k==n, 1, (m*n-m*k+1)*T[n-1, k-1, m] + (m*k-m+1)*T[n-1, k, m]];
A172018[n_]:= T[2*n-1, n, 3]/n;
Table[A172018[n], {n, 30}] (* modified by G. C. Greubel, Mar 16 2022 *)
PROG
(Sage)
@CachedFunction
def T(n, k, m):
if (k==1 or k==n): return 1
else: return (m*(n-k)+1)*T(n-1, k-1, m) + (m*k-m+1)*T(n-1, k, m)
def A172018(n): return T(2*n-1, n, 3)/n
[A172018(n) for n in (1..30)] # G. C. Greubel, Mar 16 2022
CROSSREFS
Sequence in context: A269102 A240282 A278693 * A295285 A322915 A221046
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 19 2010
EXTENSIONS
Offset changed and more terms added by G. C. Greubel, Mar 16 2022
STATUS
approved