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

0, 1, 30, 1260, 75600, 6237000, 681080400, 95351256000, 16672848192000, 3563821301040000, 914714133933600000, 277707211062240960000, 98459829376612704000000, 40319300129722902288000000, 18888041368462498071840000000, 10037644841525784689606400000000

Offset

1,3

References

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.

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.

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.

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

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

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..235

Formula

a(n) ~ sqrt(Pi) * 2^n * n^(2*n+3/2) / (3 * exp(2*n)). - Vaclav Kotesovec, Apr 25 2014

Maple

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-1), n=1..30)];

Mathematica

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;
a[n_] := T[n, n-1];
Array[a, 16] (* Jean-François Alcover, Jul 03 2019 *)

Crossrefs

A diagonal of A241171.

Sequence in context: A174716 A163521 A273416 * A358163 A107768 A353104

Adjacent sequences: A002453 A002454 A002455 * A002457 A002458 A002459

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Entry revised by N. J. A. Sloane, Apr 22 2014

Status

approved