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A097814 E.g.f. exp(3x)/(1-3x). 1

%I

%S 1,6,45,432,5265,79218,1426653,29961900,719092161,19415508030,

%T 582465299949,19221355075464,691968783248145,26986782548271978,

%U 1133444867032206045,51005019016463620932,2448240912790296851457

%N E.g.f. exp(3x)/(1-3x).

%H Michael Z. Spivey and Laura L. Steil, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Spivey/spivey7.html">The k-Binomial Transforms and the Hankel Transform</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.

%F a(n) = 3n*a(n-1)+3^n, n>0, a(0)=1; a(n) = 3^n*A000522(n).

%F G.f.: 1/Q(0), where Q(k) = 1 - 6*x*(k+1) - 9*x^2*(k+1)^2/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Sep 30 2013

%F Conjecture: a(n) +3*(-n-1)*a(n-1) +9*(n-1)*a(n-2)=0. - _R. J. Mathar_, Dec 21 2014

%t With[{nn=20},CoefficientList[Series[Exp[3x]/(1-3x),{x,0,nn}],x] Range[ 0,nn]!] (* or *) RecurrenceTable[{a[0]==1,a[n]==3n a[n-1]+3^n},a,{n,20}] (* _Harvey P. Dale_, Feb 23 2012 *)

%Y Cf. A082032.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Aug 26 2004

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Last modified September 29 05:48 EDT 2020. Contains 337425 sequences. (Running on oeis4.)