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 A049119 #24 Mar 31 2025 22:00:12
%S A049119 1,5,41,465,6721,117941,2433145,57673281,1543866945,46052954821,
%T A049119 1514472783561,54426342354385,2121878761891201,89187219264121525,
%U A049119 4020175011403931801,193438800635132796161,9895634072548245693825,536284759396849853348101,30691678336547328623916905
%N A049119 Row sums of triangle A035469.
%C A049119 Generalized Bell numbers B(4,1;n).
%D A049119 P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
%H A049119 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 A049119 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>
%H A049119 P. Blasiak, K. A. Penson and A. I. Solomon, <a href="http://arXiv.org/abs/quant-ph/0311033">Combinatorial coherent states via normal ordering of bosons</a>.
%F A049119 E.g.f.: exp(-1+1/(1-3*x)^(1/3))-1.
%F A049119 a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator (1+x)^4*d/dx. Cf. A000110, A000262, A049118 and A049120. - Peter Bala, Nov 25 2011
%F A049119 a(n) = (1/e) * (-3)^n * n! * Sum_{k>=0} binomial(-k/3,n)/k!. - _Seiichi Manyama_, Jan 17 2025
%t A049119 Drop[CoefficientList[Series[Exp[-1+1/(1-3*x)^(1/3)]-1,{x,0,19}],x]Range[0,19]!,1] (* _Stefano Spezia_, Mar 31 2025 *)
%Y A049119 Cf. Generalized Bell numbers B(m, 1, n): A049118 (m=3), this sequence (m=4), A049120 (m=5), A049412 (m=6).
%K A049119 easy,nonn
%O A049119 1,2
%A A049119 _Wolfdieter Lang_