A292871 a(n) = [x^n] (1/(1 - x - x^2/(1 - 2*x - 2*x^2/(1 - 3*x - 3*x^2/(1 - 4*x - 4*x^2/(1 - ...))))))^n.

1, 1, 5, 28, 169, 1071, 7034, 47538, 329249, 2331424, 16856915, 124387286, 936799582, 7204759238, 56634639780, 455560907508, 3755017488657, 31763254337955, 276141607672244, 2470749459597450, 22777862470135279, 216542289861590847, 2123786397875045480, 21490054470340915524, 224275454800219674782

Offset: 0

Author

Ilya Gutkovskiy, Sep 25 2017

Keywords

• nonn

Comments

a(n) is the n-th term of the n-fold convolution of Bell numbers with themselves. - Alois P. Heinz, Feb 12 2019

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..573

Crossrefs

Main diagonal of A292870.

Cf. A000110, A205574.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, `if`(k=0, 0,
     `if`(k=1, add(b(n-j, k)*binomial(n-1, j-1), j=1..n),
     (h-> add(b(j, h)*b(n-j, k-h), j=0..n))(iquo(k,2)))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);  # Alois P. Heinz, May 31 2018

Mathematica

Table[SeriesCoefficient[1/(1 - x + ContinuedFractionK[-k x^2, 1 - (k + 1) x, {k, 1, n}])^n, {x, 0, n}], {n, 0, 24}]

Formula

a(n) = A292870(n,n).

a(n) = A205574(2n,n).