This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049120 #25 Jan 17 2025 09:29:13
%S A049120 1,6,61,871,15996,358891,9509641,290528316,10051973371,388433817091,
%T A049120 16579346005806,774580047063901,39313104018590221,2153825039102763846,
%U A049120 126681355435102649161,7961385691338995966371,532402860878855993673036,37746950872336992298209151
%N A049120 Row sums of triangle A049029.
%C A049120 Generalized Bell numbers B(5,1;n).
%D A049120 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
%H A049120 W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%H A049120 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="http://www.arXiv.org/abs/quant-ph/0402027">The general boson normal ordering problem.</a>
%F A049120 E.g.f. exp(-1+1/(1-4*x)^(1/4))-1.
%F A049120 Representation of a(n) as the n-th moment of a positive function on positive half-axis (Stieltjes moment problem), in Maple notation: a(n)=int(x^n*exp(-1)*exp(-1/4*x)*(1/96*x*hypergeom([],[5/4, 3/2, 7/4, 2],1/1024*x)+ 1/8*4^(3/4)*x^(1/4)/Pi*2^(1/2)*GAMMA(3/4)*hypergeom([],[1/4, 1/2,3/4, 5/4],1/1024*x)+1/8*4^(1/2)*x^(1/2)/Pi^(1/2)*hypergeom([],[1/2, 3/4, 5/4,3/2],1/1024*x)+1/24*4^(1/4)*x^(3/4)/GAMMA(3/4)*hypergeom([],[3/4, 5/4, 3/2,7/4],1/1024*x))/x, x=0..infinity),n=1,2... . - _Karol A. Penson_, Dec 16 2007
%F A049120 a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator (1+x)^5*d/dx. Cf. A000110, A000262, A049118 and A049119. - Peter Bala, Nov 25 2011
%F A049120 a(n) = (1/e) * (-4)^n * n! * Sum_{k>=0} binomial(-k/4,n)/k!. - _Seiichi Manyama_, Jan 17 2025
%t A049120 With[{nn=20},CoefficientList[Series[Exp[-1+1/Surd[1-4x,4]]-1,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 10 2019 *)
%Y A049120 Cf. Generalized Bell numbers B(m, 1, n): A049118 (m=3), A049119 (m=4), this sequence (m=5), A049412 (m=6).
%K A049120 easy,nonn
%O A049120 1,2
%A A049120 _Wolfdieter Lang_