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A089945 Main diagonal of array A089944, in which the n-th row is the n-th binomial transform of the natural numbers. 4
1, 3, 15, 112, 1125, 14256, 218491, 3932160, 81310473, 1900000000, 49516901511, 1424099377152, 44804009850925, 1530735634132992, 56439656982421875, 2233785415175766016, 94459960699823921169, 4250383588380798812160, 202774313738037680879743 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of labeled trees on n+1 nodes with a designated node or edge. - Geoffrey Critzer, Mar 25 2017

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..386

FORMULA

a(n) = (2*n+1)*(n+1)^(n-1).

E.g.f.: (-LambertW(-x)/x)*(1-LambertW(-x))/(1+LambertW(-x)).

MATHEMATICA

nn = 30; T[z_] = -LambertW[-z]; Drop[Range[0, nn]! CoefficientList[Series[T[z] + T[z]^2/2, {z, 0, nn}], z], 1] (* Geoffrey Critzer, Mar 25 2017 *)

Table[(2 n + 1) (n + 1)^(n - 1), {n, 0, 18}] (* Michael De Vlieger, Mar 25 2017 *)

PROG

(PARI) a(n)=if(n<0, 0, (2*n+1)*(n+1)^(n-1))

(MAGMA) [(2*n+1)*(n+1)^(n-1): n in [0..50]]; // G. C. Greubel, Nov 16 2017

CROSSREFS

Cf. A089944, A089946, A245348.

Sequence in context: A001063 A130168 A267083 * A135083 A323772 A058104

Adjacent sequences:  A089942 A089943 A089944 * A089946 A089947 A089948

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 23 2003

STATUS

approved

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Last modified November 29 21:32 EST 2021. Contains 349416 sequences. (Running on oeis4.)