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A241172
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Joffe's central differences of 0: A241171(n,n-2).
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2
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0, 1, 126, 13230, 1580040, 227026800, 39502663200, 8266953895200, 2059096751712000, 603711328396176000, 206176565788633440000, 81229359235705480800000, 36597518579286942076800000, 18708155260191426661632000000, 10773738796571008900177536000000
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OFFSET
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2,3
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REFERENCES
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H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity Univ., San Antonio, TX, Vol. 2, p. 283.
S. A. Joffe, Calculation of the first thirty-two Eulerian numbers from central differences of zero, Quart. J. Pure Appl. Math. 47 (1914), 103-126.
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LINKS
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FORMULA
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a(n) ~ sqrt(Pi) * 2^n * n^(2*n+5/2) / (36 * exp(2*n)). - Vaclav Kotesovec, Apr 25 2014
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MAPLE
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T:=proc(n, k) option remember;
if k = 0 or k > n then 0
elif k=1 then 1
else k*(2*k-1)*T(n-1, k-1)+k^2*T(n-1, k); fi;
end;
[seq(T(n, n-2), n=2..30)];
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MATHEMATICA
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T[n_, k_] /; 1 <= k <= n := T[n, k] = k (2 k - 1) T[n - 1, k - 1] + k^2 T[n - 1, k]; T[_, 1] = 1; T[_, _] = 0;
a[n_] := T[n, n - 2]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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