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

1,2

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.

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)

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 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( Exp(1-(1-5*x)^(1/5)) - 1 ))); // G. C. Greubel, Oct 02 2023
(SageMath)
def A028575_list(prec):
    P.<x> = 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

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.

Sequence in context: A136729 A102773 A380310 * A368438 A006554 A052750

Adjacent sequences: A028572 A028573 A028574 * A028576 A028577 A028578

Keyword

nonn,easy,changed

Author

Wolfdieter Lang

Status

approved