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A128182
Triangle read by rows: A007318 * A128180 as infinite lower triangular matrices.
2
1, 0, 2, 1, 3, 3, 2, 6, 8, 4, 4, 12, 18, 15, 5, 8, 24, 38, 40, 24, 6, 16, 48, 78, 93, 75, 35, 7, 32, 96, 158, 202, 194, 126, 48, 8, 64, 192, 318, 423, 453, 362, 196, 63, 9, 128, 384, 638, 868, 996, 914, 622, 288, 80, 10, 256, 768, 1278, 1761, 2111, 2129, 1699, 1003, 405, 99, 11
OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
FORMULA
Equals A007318 * A128180 as infinite lower triangular matrices.
T(n,k) = Sum_{i=k..n} binomial(n,i) * A128180(i+1,k+1).
EXAMPLE
First few rows of the triangle are:
1;
0, 2;
1, 3, 3;
2, 6, 8, 4;
4, 12, 18, 15, 5;
8, 24, 38, 40, 24, 6;
16, 48, 78, 93, 75, 35, 7;
...
PROG
(PARI) \\ Here U(n, k) is A128180.
U(n, k)={(2*k-1+(-1)^(n-k)*(2*n+1))/4}
T(n, k)=sum(i=k, n, binomial(n, i)*U(i+1, k+1)) \\ Andrew Howroyd, Sep 21 2025
CROSSREFS
Row sums are A128183.
Sequence in context: A349550 A144305 A138635 * A059739 A035566 A110783
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Feb 17 2007
EXTENSIONS
a(55) onwards from Andrew Howroyd, Sep 21 2025
STATUS
approved