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URL: https://oeis.org/A039756

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A039756

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

3

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

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OFFSET

0,5

COMMENTS

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

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.

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

EXAMPLE

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;

PROG

(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))

CROSSREFS

Sequence in context: A168621 A376721 A391045 * A126065 A299427 A126062

Adjacent sequences: A039753 A039754 A039755 * A039757 A039758 A039759

KEYWORD

nonn,tabl

AUTHOR

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

STATUS

approved