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A002456 Joffe's central differences of 0, A241171(n,n-1).
(Formerly M5216 N2270)
3

%I M5216 N2270 #26 Oct 16 2023 23:26:40

%S 0,1,30,1260,75600,6237000,681080400,95351256000,16672848192000,

%T 3563821301040000,914714133933600000,277707211062240960000,

%U 98459829376612704000000,40319300129722902288000000,18888041368462498071840000000,10037644841525784689606400000000

%N Joffe's central differences of 0, A241171(n,n-1).

%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 A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 112.

%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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vaclav Kotesovec, <a href="/A002456/b002456.txt">Table of n, a(n) for n = 1..235</a>

%F a(n) ~ sqrt(Pi) * 2^n * n^(2*n+3/2) / (3 * 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-1),n=1..30)];

%t T[n_, k_] /; 1 <= k <= n := T[n, k] = k(2k-1) T[n-1, k-1] + k^2 T[n-1, k]; T[_, 1] = 1; T[_, _] = 0;

%t a[n_] := T[n, n-1];

%t Array[a, 16] (* _Jean-François Alcover_, Jul 03 2019 *)

%Y A diagonal of A241171.

%K nonn

%O 1,3

%A _N. J. A. Sloane_

%E Entry revised by _N. J. A. Sloane_, Apr 22 2014

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Last modified February 23 06:06 EST 2024. Contains 370267 sequences. (Running on oeis4.)