A241172 - OEIS

%I #18 Jul 03 2019 03:07:03

%S 0,1,126,13230,1580040,227026800,39502663200,8266953895200,

%T 2059096751712000,603711328396176000,206176565788633440000,

%U 81229359235705480800000,36597518579286942076800000,18708155260191426661632000000,10773738796571008900177536000000

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

%D 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 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 Vaclav Kotesovec, <a href="/A241172/b241172.txt">Table of n, a(n) for n = 2..236</a>

%F a(n) ~ sqrt(Pi) * 2^n * n^(2*n+5/2) / (36 * exp(2*n)). - _Vaclav Kotesovec_, Apr 25 2014

%p T:=proc(n,k) option remember;

%p if k = 0 or k > n then 0

%p elif k=1 then 1

%p else k*(2*k-1)*T(n-1,k-1)+k^2*T(n-1,k); fi;

%p end;

%p [seq(T(n,n-2),n=2..30)];

%t 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 a[n_] := T[n, n - 2]

%t Array[a, 15, 2] (* _Jean-François Alcover_, Jul 03 2019 *)

%Y A diagonal of A241171.

%K nonn

%O 2,3

%A _N. J. A. Sloane_, Apr 22 2014