A350291 a(n) = 4^n*lim_{x->0} F(2*n) where F(n) = (d/dx)F(n-1) for n >= 1 and F(0) = exp(BesselI(0, x) - 1).

1, 2, 18, 320, 9170, 376992, 20773368, 1464890856, 127857825810, 13468041055040, 1678544187282248, 243601216117107576, 40628915629002303512, 7702195195122395812600, 1644169152021779307173400, 392035147808725683863079120, 103680698454480621919621969170

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..55

Formula

The Bell formula for n > 0 is:

a(n) = Sum_{k=1..2n} Y_{2n,k}(d_i), where Y_{n,k} is the partial Bell polynomial with inputs given by d_{2i} = binomial(2i,i) and d_{2i+1} = 0. - Geoff Goehle, Mar 11 2022

Maple

F := proc(n) option remember;
ifelse(n = 0, exp(BesselI(0, x) - 1), simplify(diff(F(n-1), x))) end:
a := n -> 4^n*limit(F(2*n), x=0): seq(a(n), n = 0..16);

Mathematica

Table[Sum[BellY[n, k, Flatten[Table[{0, Binomial[j+1, (j+1)/2]}, {j, 1, n-k+1, 2}]]], {k, 0, n}], {n, 0, 32, 2}] (* Geoff Goehle, Mar 11 2022 *)

Crossrefs

Cf. A352284, row sums of A350462.

Sequence in context: A296837 A326270 A227325 * A087215 A229490 A192985

Adjacent sequences: A350288 A350289 A350290 * A350292 A350293 A350294

Keyword

nonn

Author

Peter Luschny, Mar 11 2022

Status

approved