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URL: https://oeis.org/A134836

⇱ A134836 - OEIS

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A134836
Antidiagonals of the array: A007318 * A002260(transposed).
2
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
1,5
COMMENTS
Antidiagonals tend to A001792 starting from the right: (1, 3, 8, 20, 48, 112, ...).
FORMULA
Antidiagonals of the array: A007318 * A002260(transform), where A002260 = (1; 1,2; 1,2,3; ...).
EXAMPLE
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;
...
MAPLE
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
CROSSREFS
Cf. A002260, A001792, A116445 (array transposed), A001629 (antidiagonal sums).
Sequence in context: A152720 A131247 A114278 * A180955 A349182 A191751
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, Nov 12 2007
EXTENSIONS
One term corrected by R. J. Mathar, Aug 17 2022
STATUS
approved