A226507 4*B(n+4) - (4*n+15)*B(n+3) + (n^2+8*n+9)*B(n+2) - (4*n+3)*B(n+1) + n*B(n), where B(i) are the Bell numbers A000110.

0, 0, 0, 1, 16, 177, 1726, 15912, 143148, 1279939, 11504326, 104686659, 968808308, 9144180028, 88184565504, 869867691833, 8781919559956, 90765497635245, 960434143555986, 10403548856756708, 115336464546432180, 1308260884070774299, 15177980646442995698, 180036437138753006607, 2182526416321158803528

Offset

0,5

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

B. Chern, P. Diaconis, D. M. Kane, and R. C. Rhoades, Closed expressions for averages of set partition statistics, arXiv:1304.4309 [math.CO], 2013.

Formula

a(n) ~ n^4 * Bell(n) / LambertW(n)^2 * (1 - 4/LambertW(n) + 4/LambertW(n)^2). - Vaclav Kotesovec, Jul 28 2021

Maple

A000110 := proc(n) option remember; if n <= 1 then 1 else add( binomial(n-1, i)*A000110(n-1-i), i=0..n-1); fi; end;
B:=A000110;
f:=n->4*B(n+4) - (4*n+15)*B(n+3) + (n^2+8*n+9)*B(n+2) - (4*n+3)*B(n+1) + n*B(n);
  [seq(f(n), n=0..30)];

Mathematica

Table[4 BellB[n+4] - (4 n + 15) BellB[n + 3] + (n^2 + 8 n + 9) BellB[n+2] - (4 n + 3) BellB[n+1] + n BellB[n], {n, 0, 30}] (* Vincenzo Librandi, Jul 16 2013 *)

Prog

(Magma) [4*Bell(n+4)-(4*n+15)*Bell(n+3)+(n^2+8*n+9)*Bell(n+2)-(4*n+3)*Bell(n+1)+n*Bell(n): n in [0..30]]; // Vincenzo Librandi, Jul 16 2013

Crossrefs

Cf. A000110, A200580.

Sequence in context: A007144 A017521 A323856 * A264297 A002399 A255255

Adjacent sequences: A226504 A226505 A226506 * A226508 A226509 A226510

Keyword

nonn

Author

N. J. A. Sloane, Jun 10 2013

Status

approved