A028844 Row sums of triangle A013988.

1, 6, 71, 1261, 29906, 887751, 31657851, 1318279586, 62783681421, 3365947782611, 200610405843926, 13157941480889921, 941848076798467801, 73060842413607398806, 6105266987293752470991, 546770299628690541571901, 52244284936267317229542466, 5305131708827069245129523591

Offset: 1

Author

Wolfdieter Lang

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250
• Wolfdieter Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Crossrefs

Sequences with e.g.f. exp(1-(1-m*x)^(1/m)) - 1: A000012 (m=1), A001515 (m=2), A015735 (m=3), A016036 (m=4), A028575 (m=5), this sequence (m=6).

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(1-(1-6*x)^(1/6)) -1 ))); // G. C. Greubel, Oct 03 2023

Mathematica

With[{nn=20},Rest[CoefficientList[Series[Exp[1-(1-6x)^(1/6)]-1,{x,0,nn}], x]Range[0,nn]!]] (* Harvey P. Dale, Feb 02 2012 *)

SageMath

def A028844_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( exp(1-(1-6*x)^(1/6)) -1 ).egf_to_ogf().list()
a=A028844_list(40); a[1:] # G. C. Greubel, Oct 03 2023

Formula

E.g.f.: exp(1 - (1-6*x)^(1/6)) - 1.

D-finite with recurrence: a(n) = 15*(2*n-7)*a(n-1) +5*(72*n^2-576*n+1169)*a(n-2) +45*(2*n-9)*(24*n^2-216*n+497)*a(n-3) -20*(324*n^4-6480*n^3+48735*n^2-163350*n+205877)*a(n-4) +12*(6*n-35)*(6*n-31)*(3*n-16)*(2*n-11)*(3*n-17)*a(n-5) +a(n-6). - R. J. Mathar, Jan 28 2020

From Seiichi Manyama, Jan 20 2025: (Start)

a(n) = Sum_{k=0..n} (-1)^k * 6^(n-k) * |Stirling1(n,k)| * A000587(k).

a(n) = e * (-6)^n * n! * Sum_{k>=0} (-1)^k * binomial(k/6,n)/k!. (End)