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A213560
Antidiagonal sums of the convolution array A213558.
3
1, 24, 236, 1400, 6009, 20608, 59952, 153792, 357225, 765688, 1535820, 2913560, 5270993, 9153600, 15339712, 24914112, 39357873, 60656664, 91429900, 135083256, 195987209, 279684416, 393128880, 544960000, 745814745, 1008681336, 1349297964, 1786600216, 2343221025
OFFSET
1,2
COMMENTS
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
Convolution of A000578 and A000583. - Stefano Spezia, Apr 07 2023
FORMULA
a(n) = n*(1 + n)^2*(2 + n)*(16 + 18*n + 21*n^2 + 12*n^3 + 3*n^4)/840.
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).
G.f.: x*(1 + x)*(1 + 4*x + x^2)*(1 + 10*x + x^2)/(1 - x)^9.
MATHEMATICA
(See A213558.)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jun 17 2012
STATUS
approved