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A129461 Fourth column (m=3) of triangle A129065. 3
1, 28, 908, 37896, 2036592, 138517632, 11692594944, 1202885199360, 148407122764800, 21652192199577600, 3690199478509977600, 726862474705593139200, 163918208008013340672000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
See A129065 for the M. Bruschi et al. reference.
LINKS
FORMULA
a(n) = A129065(n+3, 3), n >= 0.
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k<0 || k>n, 0, If[n==0, 1, 2*(n-1)^2*T[n-1, k] - 4*Binomial[n-1, 2]^2*T[n-2, k] +T[n-1, k-1] ]]; (* T=A129065 *)
A129461[n_]:= T[n+3, 3];
Table[A129461[n], {n, 0, 40}] (* G. C. Greubel, Feb 08 2024 *)
PROG
(Magma)
function T(n, k) // T = A129065
if k lt 0 or k gt n then return 0;
elif n eq 0 then return 1;
else return 2*(n-1)^2*T(n-1, k) - 4*Binomial(n-1, 2)^2*T(n-2, k) + T(n-1, k-1);
end if;
end function;
A129461:= func< n | T(n+3, 3) >;
[A129461(n): n in [0..20]]; // G. C. Greubel, Feb 08 2024
(SageMath)
@CachedFunction
def T(n, k): # T = A129065
if (k<0 or k>n): return 0
elif (n==0): return 1
else: return 2*(n-1)^2*T(n-1, k) - 4*binomial(n-1, 2)^2*T(n-2, k) + T(n-1, k-1)
def A129461(n): return T(n+3, 3)
[A129461(n) for n in range(41)] # G. C. Greubel, Feb 08 2024
CROSSREFS
Cf. A129065, A129460 (m=2).
Sequence in context: A095656 A057412 A160263 * A239336 A203135 A097579
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, May 04 2007
STATUS
approved

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Last modified June 22 08:18 EDT 2024. Contains 373567 sequences. (Running on oeis4.)