A213560 Antidiagonal sums of the convolution array A213558.

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..1000

Henri Muehle, Proper Mergings of Stars and Chains are Counted by Sums of Antidiagonals in Certain Convolution Arrays -- The Details, arXiv preprint arXiv:1301.1654 [math.CO], 2013.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

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

Cf. A000578, A000583, A213558, A213500.

Sequence in context: A126545 A193168 A190020 * A159506 A081863 A247825

Adjacent sequences: A213557 A213558 A213559 * A213561 A213562 A213563

Keyword

nonn,easy

Author

Clark Kimberling, Jun 17 2012

Status

approved