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a(n) = A366149(n, n).
2

%I #11 Jan 02 2024 02:43:01

%S 1,1,8,190,9080,725320,87067520,14652451360,3291452374400,

%T 951504315644800,344097665398707200,152191547632887731200,

%U 80821740082953347993600,50749489515964112842240000,37193794460546391363092480000,31464706192542487393274091520000

%N a(n) = A366149(n, n).

%C This a weighted generalized Catalan sequence (A365673) with the heptagonal numbers as weights.

%p # Using function T from A366149.

%p a := n -> T(n, n): seq(a(n), n = 0..16);

%t A366149[n_,k_]:=A366149[n,k]=Which[k==0,1,k==n,A366149[n,k-1],True,PolygonalNumber[7,n-k+1]A366149[n,k-1]+A366149[n-1,k]];

%t Array[A366149[#,#]&,20,0] (* _Paolo Xausa_, Jan 01 2024 *)

%Y Cf. A366149, A365673.

%K nonn

%O 0,3

%A _Peter Luschny_, Oct 01 2023