OFFSET
0,3
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Robert Israel, Table of n, a(n) for n = 0..420
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]
M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]
Adalbert Kerber, A matrix of combinatorial numbers related to the symmetric groups, Discrete Math., 21 (1978), 319-321.
A. Kerber, A matrix of combinatorial numbers related to the symmetric groups<, Discrete Math., 21 (1978), 319-321. [Annotated scanned copy]
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Bell polynomial
FORMULA
a(n) = sum((6^(n-m))*stirling2(n,m), m=0..n). stirling2(n,m)=A008277(n,m).
E.g.f.: exp((exp(6*x)-1)/6) satisfies A'(x)/A(x) = exp(6*x).
G.f.: T(0)/(x*(1-x)) -1/x, where T(k) = 1 - 6*x^2*(k+1)/( 6*x^2*(k+1) - (1-x-6*x*k)*(1-7*x-6*x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Oct 25 2013
a(n) = 6^n * B(n,1/6) where B(n,x) is the Bell polynomial of degree n. - Vladimir Reshetnikov, Oct 20 2015
O.g.f.: Sum_{k>=0} x^k/Product_{j=1..k} (1 - 6*j*x). - Ilya Gutkovskiy, Mar 20 2018
a(n) ~ 6^n * n^n * exp(n/LambertW(6*n) - 1/6 - n) / (sqrt(1 + LambertW(6*n)) * LambertW(6*n)^n). - Vaclav Kotesovec, Jul 15 2021
MAPLE
seq(6^n*BellB(n, 1/6), n = 0 .. 50); # Robert Israel, Oct 20 2015
MATHEMATICA
Table[6^n BellB[n, 1/6], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 20 2015 *)
PROG
(GAP) List([0..20], n->Sum([0..n], m->6^(n-m)*Stirling2(n, m))); # Muniru A Asiru, Mar 20 2018
CROSSREFS
KEYWORD
nonn,easy,eigen
AUTHOR
EXTENSIONS
a(0)=1 inserted by Alois P. Heinz, Oct 20 2015
STATUS
approved