Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #34 Apr 07 2023 11:27:24
%S 1,24,236,1400,6009,20608,59952,153792,357225,765688,1535820,2913560,
%T 5270993,9153600,15339712,24914112,39357873,60656664,91429900,
%U 135083256,195987209,279684416,393128880,544960000,745814745,1008681336,1349297964,1786600216,2343221025
%N Antidiagonal sums of the convolution array A213558.
%C An m-star is an m-antichain with a smallest element adjoined. Then, a(n) is the number of proper mergings of a 3-star and an (n-1)-chain. - _Henri Mühle_, Jan 23 2013
%C Convolution of A000578 and A000583. - _Stefano Spezia_, Apr 07 2023
%H Clark Kimberling, <a href="/A213560/b213560.txt">Table of n, a(n) for n = 1..1000</a>
%H Henri Muehle, <a href="http://arxiv.org/abs/1301.1654">Proper Mergings of Stars and Chains are Counted by Sums of Antidiagonals in Certain Convolution Arrays -- The Details</a>, arXiv preprint arXiv:1301.1654 [math.CO], 2013.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n) = n*(1 + n)^2*(2 + n)*(16 + 18*n + 21*n^2 + 12*n^3 + 3*n^4)/840.
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
%F G.f.: x*(1 + x)*(1 + 4*x + x^2)*(1 + 10*x + x^2)/(1 - x)^9.
%t (See A213558.)
%Y Cf. A000578, A000583, A213558, A213500.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Jun 17 2012