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 A039756 Triangle of B-analogs of Stirling numbers of 2nd kind. 3

%I

%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 R. 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)

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Last modified May 16 17:22 EDT 2021. Contains 343949 sequences. (Running on oeis4.)