A246307 Numerator of Z^(2)(n), where Z^(2)(n) = n for n=0,1; thereafter Z^(2)(n) = (1/3)*Sum_{k=1..n-1} Stirling_2(n,k)*Z^(2)(k).

0, 1, 1, 5, 6, 399, 10137, 364737, 2206077, 276269667, 21732613641, 2097942773859, 60958311638283, 16792338947372883, 2704712327221326273, 503673752669173980741, 6711263837756846638875, 3248087145389524173611367, 885435154962504420364992693, 270090359296255369532260168299

Offset

0,4

Comments

The denominators are various powers of 2.

Links

Table of n, a(n) for n=0..19.

D. Barsky, J.-P. Bézivin, p-adic Properties of Lengyel's Numbers, Journal of Integer Sequences, 17 (2014), #14.7.3.

Example

The sequence Z^(2)(n) begins 0, 1, 1/2, 5/4, 6, 399/8, 10137/16, 364737/32, 2206077/8, 276269667/32,  21732613641/64, 2097942773859/128, 60958311638283/64, 16792338947372883/256,  2704712327221326273/512,...

Maple

Z:=proc(n, p) option remember; local k; if n <= 1 then n else add(stirling2(n, k)*Z(k, p)/(p-1), k=1..n-1); fi; end;
t1:=[seq(Z(n, 2), n=0..35)];

Crossrefs

Cf. A005121.

Sequence in context: A007666 A064177 A042721 * A269588 A048658 A001111

Adjacent sequences: A246304 A246305 A246306 * A246308 A246309 A246310

Keyword

nonn

Author

N. J. A. Sloane, Aug 22 2014

Status

approved