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A039756 Triangle of B-analogs of Stirling numbers of 2nd kind.

%I A039756 #31 Mar 14 2024 11:11:42
%S A039756 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 A039756 1771,364,1,1,49,791,5075,12411,9219,1093,1,1,64,1428,13776,58086,
%U A039756 96096,47188,3280,1,1,81,2388,32340,209622,618870,719860,239220,9841,1
%N A039756 Triangle of B-analogs of Stirling numbers of 2nd kind.
%C A039756 This is a variant of A039755 with reflected rows. - _Tilman Piesk_, Oct 27 2019
%H A039756 Alois P. Heinz, <a href="/A039756/b039756.txt">Rows n = 0..100, flattened</a>
%H A039756 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 A039756 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 A039756 Sum a(n,n-k) x^n*y^k/n! = exp(x + y/2*(exp(2*x) - 1)).
%F A039756 T(n, k) = A039755(n, n-k). - _Tilman Piesk_, Oct 27 2019
%e A039756 1;
%e A039756 1,  1;
%e A039756 1,  4,   1;
%e A039756 1,  9,  13,    1;
%e A039756 1, 16,  58,   40,     1;
%e A039756 1, 25, 170,  330,   121,    1;
%e A039756 1, 36, 395, 1520,  1771,  364,    1;
%e A039756 1, 49, 791, 5075, 12411, 9219, 1093,  1;
%o A039756 (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 A039756 Cf. A039755.
%K A039756 nonn,tabl
%O A039756 0,5
%A A039756 Ruedi Suter (suter(AT)math.ethz.ch)