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A098558
Expansion of e.g.f. (1+x)/(1-x).
21
1, 2, 4, 12, 48, 240, 1440, 10080, 80640, 725760, 7257600, 79833600, 958003200, 12454041600, 174356582400, 2615348736000, 41845579776000, 711374856192000, 12804747411456000, 243290200817664000, 4865804016353280000, 102181884343418880000, 2248001455555215360000
OFFSET
0,2
COMMENTS
Essentially the same as A052849: a(0)=0 and a(n) = A052849(n) for n>=1.
Equals row sums (unsigned) of triangle A158471. - Gary W. Adamson, Mar 20 2009
Also the number of graceful labelings of the star graph on n+1 nodes. - Eric W. Weisstein, Mar 31 2020
LINKS
Eric Weisstein's World of Mathematics, Graceful Labeling
Eric Weisstein's World of Mathematics, Star Graph
FORMULA
a(n) = 2*n! - 0^n.
a(n) = Sum_{k=0..n} (k+1) * A008290(n,k). - Alois P. Heinz, Mar 11 2022
Sum_{n>=0} 1/a(n) = (e+1)/2. - Amiram Eldar, Feb 02 2023
a(n) = HypergeomRegularized([1, -n], [2 - n], -1). - Peter Luschny, Apr 26 2024
MATHEMATICA
Join[{1}, 2*Range[30]!] (* G. C. Greubel, Jan 17 2018 *)
With[{nn=30}, CoefficientList[Series[(1+x)/(1-x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jun 05 2021 *)
a[n_] := Hypergeometric2F1Regularized[1, -n, 2 - n, -1];
Table[a[n], {n, 0, 22}] (* Peter Luschny, Apr 26 2024 *)
PROG
(PARI) concat([1], vector(30, n, 2*n!)) \\ G. C. Greubel, Jan 17 2018
(Magma) [1] cat [2*Factorial(n): n in [1..30]]; // G. C. Greubel, Jan 17 2018
(SageMath)
CF = ComplexBallField(100)
def a(n):
return Integer(CF(-1).hypergeometric([1, -n], [2 - n], regularized=True))
print([a(n) for n in range(23)]) # Peter Luschny, Apr 26 2024
CROSSREFS
Row sums of A008518 and of A128564.
Cf. A158471.
Sequence in context: A013172 A321009 A052849 * A152827 A030813 A126772
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 14 2004
STATUS
approved