A134836
Antidiagonals of the array: A007318 * A002260(transposed).
Original entry on oeis.org
1, 1, 1, 1, 3, 1, 1, 5, 3, 1, 1, 7, 8, 3, 1, 1, 9, 16, 8, 3, 1, 1, 11, 27, 20, 8, 3, 1, 1, 13, 41, 43, 20, 8, 3, 1, 1, 15, 58, 81, 48, 20, 8, 3, 1, 1, 17, 78, 138, 106, 48, 20, 8, 3, 1, 1, 19, 101, 218, 213, 112, 48, 20, 8, 3, 1
Offset: 1
First few rows of the array:
1, 1, 1, 1, 1, 1, ...;
1, 3, 3, 3, 3, 3, ...;
1, 5, 8, 8, 8, 8, ...;
1, 7, 16, 20, 20, 20, ...;
1, 9, 27, 43, 48, 48, ...;
1, 11, 41, 81, 106, 112, ...;
...
First few rows of the triangle:
1;
1, 1;
1, 3, 1;
1, 5, 3, 1;
1, 7, 8, 3, 1;
1, 9, 16, 8, 3, 1;
1, 11, 27, 20, 8, 3, 1;
1, 13, 41, 43, 20, 8, 3, 1;
...
-
A002260 := proc(n,k)
if n <= k then
n+1;
else
0 ;
end if;
end proc:
A007318 := proc(n,k)
if k <= n then
binomial(n,k) ;
else
0
end if;
end proc:
A134836 := proc(n,k)
add( A007318(n,i)*A002260(i,k),i=0..k) ;
end proc:
seq(seq(A134836(d-k,k),k=0..d),d=0..12) ; # R. J. Mathar, Aug 17 2022
A139488
Binomial transform of [1, 2, 3, 4, 0, 0, 0, ...].
Original entry on oeis.org
1, 3, 8, 20, 43, 81, 138, 218, 325, 463, 636, 848, 1103, 1405, 1758, 2166, 2633, 3163, 3760, 4428, 5171, 5993, 6898, 7890, 8973, 10151, 11428, 12808, 14295, 15893, 17606, 19438, 21393, 23475, 25688, 28036, 30523, 33153, 35930, 38858, 41941, 45183
Offset: 0
a(5) = 43 = (1, 4, 6, 4, 1) dot (1, 2, 3, 4, 0) = (1 + 8, + 18 + 16 + 0).
-
a:=proc(n) options operator, arrow: (2/3)*n^3-(1/2)*n^2+(11/6)*n+1 end proc: seq(a(n),n=0..35); # Emeric Deutsch, Apr 30 2008
-
f[n_] := Plus @@ (Table[ Binomial[n - 1, i], {i, 0, n - 1}] PadRight[{1, 2, 3, 4}, n]); Array[f, 43] (* Robert G. Wilson v, Apr 24 2008 *)
Showing 1-2 of 2 results.
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