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

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, 1771, 364, 1, 1, 49, 791, 5075, 12411, 9219, 1093, 1, 1, 64, 1428, 13776, 58086, 96096, 47188, 3280, 1, 1, 81, 2388, 32340, 209622, 618870, 719860, 239220, 9841, 1

Offset: 0

Author

Ruedi Suter (suter(AT)math.ethz.ch)

Keywords

• nonn
• tabl

Comments

This is a variant of A039755 with reflected rows. - Tilman Piesk, Oct 27 2019

Examples

			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,  1771,  364,    1;
1, 49, 791, 5075, 12411, 9219, 1093,  1;
		

Links

• Alois P. Heinz, Rows n = 0..100, flattened
• Paweł Hitczenko, A class of polynomial recurrences resulting in (n/log n, n/log^2 n)-asymptotic normality, arXiv:2403.03422 [math.CO], 2024. See p. 8.
• Ruedi Suter, Two analogues of a classical sequence, J. Integer Sequences, Vol. 3 (2000), #P00.1.8.

Crossrefs

Cf. A039755.

Programs

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))

Formula

Sum a(n,n-k) x^n*y^k/n! = exp(x + y/2*(exp(2*x) - 1)).

T(n, k) = A039755(n, n-k). - Tilman Piesk, Oct 27 2019