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A172013
a(n) = 6*A142459(2*n, n)/(n+1).
1
3, 118, 20343, 8530698, 6711481694, 8575821262764, 16243345162977759, 42826533033277249154, 150138953276380791799098, 675925071086215282939520628, 3802445616812067139270851537718, 26147695687370407271086390933321188, 215852465255521412471161891166554453788
OFFSET
1,1
LINKS
FORMULA
a(n) = 6*A142459(2*n, n)/(n+1).
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]];
A142459[n_, k_]:= A142459[n, k]= T[n, k, 4];
A172013[n_]:= A172013[n]= 6*A142459[2*n, n]/(n+1);
Table[A172013[n], {n, 30}] (* modified by G. C. Greubel, Mar 18 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 A142459(n, k): return T(n, k, 4)
def A172013(n): return 6*A142459(2*n, n)/(n+1)
[A172013(n) for n in (1..30)] # G. C. Greubel, Mar 18 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 19 2010
EXTENSIONS
Offset and formula corrected by G. C. Greubel, Mar 18 2022
STATUS
approved