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

1,2

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.

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)

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 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(1-(1-6*x)^(1/6)) -1 ))); // G. C. Greubel, Oct 03 2023
(SageMath)
def A028844_list(prec):
    P.<x> = 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

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).

Sequence in context: A341967 A371366 A092085 * A274644 A349684 A349598

Adjacent sequences: A028841 A028842 A028843 * A028845 A028846 A028847

Keyword

nonn,changed

Author

Wolfdieter Lang

Status

approved