A028575 Row sums of triangle A011801.

1, 5, 49, 721, 14177, 349141, 10334689, 357361985, 14137664833, 629779342213, 31195027543505, 1700812505769169, 101218448336028193, 6528869281965115541, 453720852957751220353, 33796334125623555379969, 2686138908337714715560577, 226908450494953996837748869

Offset: 1

Author

Wolfdieter Lang

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• 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), this sequence (m=5), A028844 (m=6).

Cf. A011801.

Programs

Magma

R:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(1-(1-5*x)^(1/5)) - 1 ))); // G. C. Greubel, Oct 02 2023

Mathematica

Rest[With[{nn=20},CoefficientList[Series[Exp[1-(1-5x)^(1/5)]-1, {x,0,nn}], x] Range[0,nn]!]] (* Harvey P. Dale, Aug 02 2016 *)

SageMath

def A028575_list(prec):
    P. = PowerSeriesRing(QQ, prec)
    return P( exp(1-(1-5*x)^(1/5)) -1 ).egf_to_ogf().list()
a=A028575_list(40); a[1:] # G. C. Greubel, Oct 02 2023

Formula

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

a(n) = D^n(exp(x)) evaluated at x = 0, where D is the operator 1/(1-x)^4*d/dx. Cf. A001515, A015735 and A016036. - Peter Bala, Nov 25 2011

D-finite with recurrence: a(n) -20*(n-3)*a(n-1) +30*(5*n^2-35*n +62)*a(n-2) -100*(n-4)*(5*n^2-40*n+81)*a(n-3) +(5*n-22)*(5*n-21)*(5*n-24)*(5*n-23)*a(n-4) -a(n-5) = 0. - R. J. Mathar, Jan 28 2020

From Seiichi Manyama, Jan 20 2025: (Start)

a(n) = Sum_{k=0..n} (-1)^k * 5^(n-k) * |Stirling1(n,k)| * A000587(k).

a(n) = e * (-5)^n * n! * Sum_{k>=0} (-1)^k * binomial(k/5,n)/k!. (End)