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 A005012 Shifts one place left under 6th order binomial transform. (Formerly M4434) 11
 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. [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 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 Cf. A004211. Sequence in context: A199564 A225032 A124403 * A123784 A091695 A002882 Adjacent sequences:  A005009 A005010 A005011 * A005013 A005014 A005015 KEYWORD nonn,easy,eigen AUTHOR EXTENSIONS a(0)=1 inserted by Alois P. Heinz, Oct 20 2015 STATUS approved

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Last modified October 20 10:32 EDT 2019. Contains 328257 sequences. (Running on oeis4.)