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

0, 1, 126, 13230, 1580040, 227026800, 39502663200, 8266953895200, 2059096751712000, 603711328396176000, 206176565788633440000, 81229359235705480800000, 36597518579286942076800000, 18708155260191426661632000000, 10773738796571008900177536000000

Offset: 2

Author

N. J. A. Sloane, Apr 22 2014

Keywords

• nonn

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.
• 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.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 2..236

Crossrefs

A diagonal of A241171.

Programs

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-2),n=2..30)];

Mathematica

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]
Array[a, 15, 2] (* Jean-François Alcover, Jul 03 2019 *)

Formula

a(n) ~ sqrt(Pi) * 2^n * n^(2*n+5/2) / (36 * exp(2*n)). - Vaclav Kotesovec, Apr 25 2014