A128182 Triangle read by rows: A007318 * A128180 as infinite lower triangular matrices.

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.

Cf. A007318, A128179, A128180.

Sequence in context: A349550 A144305 A138635 * A059739 A035566 A110783

Adjacent sequences: A128179 A128180 A128181 * A128183 A128184 A128185

Keyword

nonn,tabl

Author

Gary W. Adamson, Feb 17 2007

Extensions

a(55) onwards from Andrew Howroyd, Sep 21 2025

Status

approved