A134083 A007318 * A134082.

1, 3, 1, 5, 6, 1, 7, 15, 9, 1, 9, 28, 30, 12, 1, 11, 45, 70, 50, 15, 1, 13, 66, 135, 140, 75, 18, 1, 15, 91, 231, 315, 245, 105, 21, 1, 17, 120, 364, 616, 630, 392, 140, 24, 1, 19, 153, 540, 1092, 1386, 1134, 588, 180, 27, 1

Offset: 0

Author

Gary W. Adamson, Oct 07 2007

Keywords

• nonn
• tabl

Comments

Row sums = A001787: (1, 4, 12, 32, 80, 192, ...).

A134083 * [1,2,3,...] = A084850: (1, 5, 20, 68, 208, 592, ...).

Examples

			First few rows of the triangle:
   1;
   3,  1;
   5,  6,   1;
   7, 15,   9,   1;
   9, 28,  30,  12,   1;
  11, 45,  70,  50,  15,   1;
  13, 66, 135, 140,  75,  18,  1;
  15, 91, 231, 315, 245, 105, 21, 1;
  ...
		

Crossrefs

Cf. A134082, A001787, A084850.

Formula

Binomial transform of A134082

From formalism in A132382, e.g.f. = I_o[2*(u*x)^(1/2)] exp(x)(1+2x) where I_o is the zeroth modified Bessel function of the first kind, i.e., I_o[2*(u*x)^(1/2)] = Sum_{j>=0} u^j/j! * x^j/j!. - Tom Copeland, Dec 07 2007

Row polynomial e.g.f.: exp(x*y) * exp(x) * (1+2x). - Tom Copeland, Dec 03 2013