A185905 Rectangular array binomial(k+3,4)*binomial(n+3,4), by antidiagonals.

1, 5, 5, 15, 25, 15, 35, 75, 75, 35, 70, 175, 225, 175, 70, 126, 350, 525, 525, 350, 126, 210, 630, 1050, 1225, 1050, 630, 210, 330, 1050, 1890, 2450, 2450, 1890, 1050, 330, 495, 1650, 3150, 4410, 4900, 4410, 3150, 1650, 495, 715, 2475, 4950, 7350, 8820, 8820, 7350, 4950, 2475, 715, 1001, 3575, 7425, 11550

Offset: 1

Author

Clark Kimberling, Feb 06 2011

Keywords

• nonn
• tabl

Comments

A member of the accumulation chain ... < A185906 < A000007 < A000012 < A003991 < A098358 < A185904 < A185905 < ... (See A144112 for the definition of accumulation array.)

Examples

			Northwest corner:
   1,    5,   15,   35,   70
   5,   25,   75,  175,  350
  15,   75,  225,  525, 1050
  35,  175,  425, 1225, 2450
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A144112.

Row 1 = Column 1 = A000332.

Programs

Mathematica

a[n_, k_] := Binomial[k + 3, 4]*Binomial[n + 3, 4]; Table[a[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 22 2017 *)

Formula

T(n,k) = binomial(k+3,4)*binomial(n+3,4), k >= 1, n >= 1.