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A005012 Shifts one place left under 6th order binomial transform.
(Formerly M4434)
9
1, 1, 7, 55, 505, 5497, 69823, 1007407, 16157905, 284214097, 5432922775, 112034017735, 2476196276617, 58332035387017, 1457666574447247, 38485034941511935, 1069787864231083297, 31213730550761076769, 953352927192964243879, 30406448846308128741847 (list; graph; refs; listen; history; text; internal format)
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.

Adalbert Kerber, A matrix of combinatorial numbers related to the symmetric groups, Discrete Math., 21 (1978), 319-321.

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

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 *)

CROSSREFS

Cf. A004211.

Sequence in context: A199564 A225032 A124403 * A123784 A091695 A002882

Adjacent sequences:  A005009 A005010 A005011 * A005013 A005014 A005015

KEYWORD

nonn,easy,eigen

AUTHOR

N. J. A. Sloane, Simon Plouffe

EXTENSIONS

a(0)=1 inserted by Alois P. Heinz, Oct 20 2015

STATUS

approved

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Last modified April 24 00:59 EDT 2017. Contains 285338 sequences.