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Row sums of triangle A011801.
6

%I #23 Oct 03 2023 10:50:29

%S 1,5,49,721,14177,349141,10334689,357361985,14137664833,629779342213,

%T 31195027543505,1700812505769169,101218448336028193,

%U 6528869281965115541,453720852957751220353,33796334125623555379969

%N Row sums of triangle A011801.

%H Vincenzo Librandi, <a href="/A028575/b028575.txt">Table of n, a(n) for n = 1..200</a>

%H Wolfdieter Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

%F E.g.f.: exp(1 - (1-5*x)^(1/5)) - 1.

%F a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator 1/(1-x)^4*d/dx. Cf. A001515, A015735 and A016036. - _Peter Bala_, Nov 25 2011

%F D-finite with recurrence: a(n) -20*(n-3)*a(n-1) +30*(5*n^2-35*n +62)*a(n-2) -100*(n-4)*(5*n^2-40*n+81)*a(n-3) +(5*n-22)*(5*n-21)*(5*n-24)*(5*n-23)*a(n-4) -a(n-5) = 0. - _R. J. Mathar_, Jan 28 2020

%t Rest[With[{nn=20},CoefficientList[Series[Exp[1-(1-5x)^(1/5)]-1, {x,0,nn}], x] Range[0,nn]!]] (* _Harvey P. Dale_, Aug 02 2016 *)

%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(1-(1-5*x)^(1/5)) - 1 ))); // _G. C. Greubel_, Oct 02 2023

%o (SageMath)

%o def A028575_list(prec):

%o P.<x> = PowerSeriesRing(QQ, prec)

%o return P( exp(1-(1-5*x)^(1/5)) -1 ).egf_to_ogf().list()

%o a=A028575_list(40); a[1:] # _G. C. Greubel_, Oct 02 2023

%Y Sequences with e.g.f. exp(1-(1-m*x)^(1/m)) - 1: A000012 (m=1), A001515 (m=2), A015735 (m=3), A016036 (m=4), this sequence (m=5), A028844 (m=6).

%Y Cf. A011801.

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_