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A385577 Array read by ascending antidiagonals: A(n,m) = n*Pochhammer(n+1,m+1)/(m+2).

%I A385577 #7 Jul 07 2025 00:41:46
%S A385577 0,1,0,3,2,0,6,8,6,0,10,20,30,24,0,15,40,90,144,120,0,21,70,210,504,
%T A385577 840,720,0,28,112,420,1344,3360,5760,5040,0,36,168,756,3024,10080,
%U A385577 25920,45360,40320,0,45,240,1260,6048,25200,86400,226800,403200,362880,0
%N A385577 Array read by ascending antidiagonals: A(n,m) = n*Pochhammer(n+1,m+1)/(m+2).
%D A385577 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 20.
%H A385577 Paul W. Haggard and Bonnie L. Sadler, <a href="https://doi.org/10.1080/0020739940250205">A Generalization of Triangular Numbers</a>, International Journal of Mathematical Education in Science and Technology 25 (2): 195-202, (1994).
%F A385577 Sum_{m=0..n} A(n-m,m) = A006231(n+1).
%F A385577 A(n,1) = A007290(n+2).
%F A385577 A(1,n) = A000142(n+1).
%F A385577 A(2,n) = A001048(n+2).
%F A385577 A(3,n) = abs(A238474(n+1)).
%F A385577 A(n,n) = n!*A002740(n+2)
%e A385577 Array begins as:
%e A385577    0,  0,   0,    0,     0,     0,      0, ...
%e A385577    1,  2,   6,   24,   120,   720,   5040, ...
%e A385577    3,  8,  30,  144,   840,  5760,  45360, ...
%e A385577    6, 20,  90,  504,  3360, 25920, 226800, ...
%e A385577   10, 40, 210, 1344, 10080, 86400, 831600, ...
%e A385577   ...
%t A385577 A[n_,m_]:=n*Pochhammer[n+1,m+1]/(m+2); Table[A[n-m,m],{n,0,9},{m,0,n}]//Flatten
%Y A385577 Cf. A000142, A001048, A002740, A006231, A007290, A068424, A238474.
%Y A385577 Cf. A000217 (m=0), A033487 (m=2), A158874 (m=3).
%Y A385577 Cf. A000004 (n=0).
%K A385577 nonn,easy,tabl
%O A385577 0,4
%A A385577 _Stefano Spezia_, Jul 03 2025