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A028844
Row sums of triangle A013988.
5
1, 6, 71, 1261, 29906, 887751, 31657851, 1318279586, 62783681421, 3365947782611, 200610405843926, 13157941480889921, 941848076798467801, 73060842413607398806, 6105266987293752470991, 546770299628690541571901
OFFSET
1,2
LINKS
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
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
KEYWORD
nonn
STATUS
approved