|
%I #31 Mar 14 2024 11:11:42
%S 1,1,1,1,4,1,1,9,13,1,1,16,58,40,1,1,25,170,330,121,1,1,36,395,1520,
%T 1771,364,1,1,49,791,5075,12411,9219,1093,1,1,64,1428,13776,58086,
%U 96096,47188,3280,1,1,81,2388,32340,209622,618870,719860,239220,9841,1
%N Triangle of B-analogs of Stirling numbers of 2nd kind.
%C This is a variant of A039755 with reflected rows. - _Tilman Piesk_, Oct 27 2019
%H Alois P. Heinz, <a href="/A039756/b039756.txt">Rows n = 0..100, flattened</a>
%H Paweł Hitczenko, <a href="https://arxiv.org/abs/2403.03422">A class of polynomial recurrences resulting in (n/log n, n/log^2 n)-asymptotic normality</a>, arXiv:2403.03422 [math.CO], 2024. See p. 8.
%H Ruedi Suter, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/SUTER/sut1.html">Two analogues of a classical sequence</a>, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.
%F Sum a(n,n-k) x^n*y^k/n! = exp(x + y/2*(exp(2*x) - 1)).
%F T(n, k) = A039755(n, n-k). - _Tilman Piesk_, Oct 27 2019
%e 1;
%e 1, 1;
%e 1, 4, 1;
%e 1, 9, 13, 1;
%e 1, 16, 58, 40, 1;
%e 1, 25, 170, 330, 121, 1;
%e 1, 36, 395, 1520, 1771, 364, 1;
%e 1, 49, 791, 5075, 12411, 9219, 1093, 1;
%o (PARI) T(n,k)=if(k<0||k>n,0,n!*polcoeff(polcoeff(exp(x*y+(exp(2*x*y+x*O(x^n))-1)/(2*y)),n),k))
%Y Cf. A039755.
%K nonn,tabl
%O 0,5
%A Ruedi Suter (suter(AT)math.ethz.ch)
|
