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Triangle read by rows, T(n, k) = A243664(n) * binomial(n, k).
3

%I #6 May 10 2023 11:50:15

%S 1,1,1,21,42,21,1849,5547,5547,1849,426405,1705620,2558430,1705620,

%T 426405,203374081,1016870405,2033740810,2033740810,1016870405,

%U 203374081,173959321557,1043755929342,2609389823355,3479186431140,2609389823355,1043755929342,173959321557

%N Triangle read by rows, T(n, k) = A243664(n) * binomial(n, k).

%e [0] 1;

%e [1] 1, 1;

%e [2] 21, 42, 21;

%e [3] 1849, 5547, 5547, 1849;

%e [4] 426405, 1705620, 2558430, 1705620, 426405;

%e [5] 203374081, 1016870405, 2033740810, 2033740810, 1016870405, 203374081;

%o (SageMath) # uses[TransOrdPart from A362585]

%o def A362849(n) -> list[int]: return TransOrdPart(3, n)

%o for n in range(6): print(A362849(n))

%Y Family of triangles: A055372 (m=0, Pascal), A362585 (m=1, Fubini), A362586 (m=2, Joffe), this sequence (m=3, A278073).

%Y Cf. A243664 (column 0 and main diagonal).

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, May 05 2023