A205543 Logarithmic derivative of the Bell numbers (A000110).

1, 3, 10, 39, 171, 822, 4271, 23759, 140518, 878883, 5789015, 40019058, 289513303, 2186421919, 17199606090, 140662816543, 1193865048363, 10499107480518, 95528651305671, 898071593401559, 8712429618413678, 87118795125708283, 896925422648691735

Offset: 1

Author

Paul D. Hanna, Jan 28 2012

Keywords

• nonn

Comments

a(n) = number of indecomposable partitions (A074664) of [n+3] in which n+3 lies in a doubleton block (see Link). - David Callan, Oct 08 2014

Examples

			L.g.f.: L(x) = x + 3*x^2/2 + 10*x^3/3 + 39*x^4/4 + 171*x^5/5 + 822*x^6/6 +...
where exponentiation yields the o.g.f. of the Bell numbers:
exp(L(x)) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 52*x^5 + 203*x^6 + 877*x^7 +...
which equals the series:
exp(L(x)) = 1 + x/(1-x) + x^2/((1-x)*(1-2*x)) + x^3/((1-x)*(1-2*x)*(1-3*x)) +...
		

Links

• David Callan, A combinatorial interpretation for this sequence

Crossrefs

Cf. A000110.

Programs

PARI

{a(n)=n*polcoeff(log(sum(m=0,n, x^m/prod(k=1,m, 1-k*x +x*O(x^n)))),n)}

Formula

L.g.f.: log( Sum_{n>=0} x^n / Product_{k=1..n} (1 - k*x) ).