A049412 Row sums of triangle A049385.

1, 7, 85, 1465, 32677, 894103, 28977817, 1085272945, 46112305897, 2191384887175, 115164935076445, 6631403822046697, 415179375712149517, 28079663069162365207, 2040146099677929685345, 158473205735310372796897, 13105410949812720002967889, 1149574078597445578977405319

Offset: 1

Author

Wolfdieter Lang

Keywords

• nonn

Comments

Generalized Bell numbers B(6,1;n).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..360
• P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, Phys. Lett. A 309 (2003) 198-205.
• P. Blasiak, K. A. Penson and A. I. Solomon, The general boson normal ordering problem, arXiv:quant-ph/0402027, 2004.
• W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Crossrefs

Cf. Generalized Bell numbers B(m, 1, n): A049118 (m=3), A049119 (m=4), A049120 (m=5), this sequence (m=6).

Programs

Mathematica

terms = 16;
Rest[CoefficientList[Exp[-1+1/(1-5x)^(1/5)]-1+O[x]^(terms+1), x]] Range[ terms]! (* Jean-François Alcover, Nov 11 2018 *)

Formula

E.g.f.: exp(-1+1/(1-5*x)^(1/5))-1.

a(n) = (1/e) * (-5)^n * n! * Sum_{k>=0} binomial(-k/5,n)/k!. - Seiichi Manyama, Jan 17 2025