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

1,2

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.

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

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 *)

Crossrefs

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

Sequence in context: A317353 A302565 A369372 * A346984 A361065 A056547

Adjacent sequences: A049409 A049410 A049411 * A049413 A049414 A049415

Keyword

nonn

Author

Wolfdieter Lang

Status

approved