A173110 Given triangle A173108 = M, then A173110 = Lim_{n->inf.} M^n; the left-shifted vector considered as a sequence.

1, 1, 3, 6, 20, 60, 230, 950, 4420, 22230, 120914, 702820, 4343860, 28393280, 195492054

Offset: 0

Author

Gary W. Adamson, Feb 09 2010

Keywords

• nonn

Comments

Triangle A173108 as an infinite lower triangular matrix * A173110 = A173110;

i.e. the sequence remains unchanged.

Contribution from Gary W. Adamson, Jul 08 2010: (Start)

Let B(x) = (1 + x + 2x^2 + 5x^3 + 15x^4 + ...), Bell numbers, A000110; and

A(x) = (1 + x + 3x^2 + 6x^3 + 20x^4 + ...). Then A(x) = B(x) * B(x^2) *

B(x^4) * B(x^8) * ...; and B(x) = A(x)/A(x^2). (End)

Crossrefs

A173108, A173111

Cf. A000110 [From Gary W. Adamson, Jul 08 2010]

Formula

Given triangle A173108 = M, then A173110 = Lim_{n->inf.} M^n; the left-shifted vector considered as a sequence