A049119 Row sums of triangle A035469.

1, 5, 41, 465, 6721, 117941, 2433145, 57673281, 1543866945, 46052954821, 1514472783561, 54426342354385, 2121878761891201, 89187219264121525, 4020175011403931801, 193438800635132796161, 9895634072548245693825

Offset

1,2

Comments

Generalized Bell numbers B(4,1;n).

References

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.

Links

Table of n, a(n) for n=1..17.

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem.

P. Blasiak, K. A. Penson and A. I. Solomon, Combinatorial coherent states via normal ordering of bosons.

Formula

E.g.f.: exp(-1+1/(1-3*x)^(1/3))-1.

a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator (1+x)^4*d/dx. Cf. A000110, A000262, A049118 and A049120. - Peter Bala, Nov 25 2011

Crossrefs

Cf. A049118, generalized Bell numbers B(3, 1, n). A049120.

Sequence in context: A047735 A096364 A210661 * A367423 A332236 A305981

Adjacent sequences: A049116 A049117 A049118 * A049120 A049121 A049122

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved