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A241172 Joffe's central differences of 0: A241171(n,n-2).

%I A241172 #18 Jul 03 2019 03:07:03
%S A241172 0,1,126,13230,1580040,227026800,39502663200,8266953895200,
%T A241172 2059096751712000,603711328396176000,206176565788633440000,
%U A241172 81229359235705480800000,36597518579286942076800000,18708155260191426661632000000,10773738796571008900177536000000
%N A241172 Joffe's central differences of 0: A241171(n,n-2).
%D A241172 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.
%D A241172 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.
%H A241172 Vaclav Kotesovec, <a href="/A241172/b241172.txt">Table of n, a(n) for n = 2..236</a>
%F A241172 a(n) ~ sqrt(Pi) * 2^n * n^(2*n+5/2) / (36 * exp(2*n)). - _Vaclav Kotesovec_, Apr 25 2014
%p A241172 T:=proc(n,k) option remember;
%p A241172 if k = 0 or k > n then 0
%p A241172 elif k=1 then 1
%p A241172 else k*(2*k-1)*T(n-1,k-1)+k^2*T(n-1,k); fi;
%p A241172 end;
%p A241172 [seq(T(n,n-2),n=2..30)];
%t A241172 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;
%t A241172 a[n_] := T[n, n - 2]
%t A241172 Array[a, 15, 2] (* _Jean-François Alcover_, Jul 03 2019 *)
%Y A241172 A diagonal of A241171.
%K A241172 nonn
%O A241172 2,3
%A A241172 _N. J. A. Sloane_, Apr 22 2014