A382629 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = (n-k)*T(n-1,k-1) + 2*(k+1)*T(n-1,k) + A102365(n,k) with T(n,k) = 0 if k < 0 or k > n.

1, 3, 0, 7, 4, 0, 15, 35, 5, 0, 31, 203, 115, 6, 0, 63, 994, 1428, 315, 7, 0, 127, 4470, 13421, 7450, 783, 8, 0, 255, 19185, 108156, 121314, 32865, 1839, 9, 0, 511, 80161, 793704, 1593902, 870191, 130665, 4171, 10, 0, 1023, 329648, 5483093, 18269658, 17591035, 5383906, 485166, 9251, 11, 0

Offset: 0

Author

Seiichi Manyama, Apr 01 2025

Keywords

• nonn
• tabl

Examples

			Triangle begins:
    1;
    3,     0;
    7,     4,      0;
   15,    35,      5,       0;
   31,   203,    115,       6,      0;
   63,   994,   1428,     315,      7,      0;
  127,  4470,  13421,    7450,    783,      8,    0;
  255, 19185, 108156,  121314,  32865,   1839,    9,  0;
  511, 80161, 793704, 1593902, 870191, 130665, 4171, 10, 0;
  ...
		

Links

• Seiichi Manyama, Rows n = 0..139, flattened

Crossrefs

Row sums give A180875.

Column k=0 gives A126646.

Cf. A098830, A102365.

Programs

PARI

a102365(n, k) = if(k==0, 1, if(nn, 0, (n-k)*T(n-1, k-1)+2*(k+1)*T(n-1, k)+a102365(n, k));

Formula

(2/3)^n * Sum_{k=0..n} T(n,k)/2^k = A098830(n).