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A185905 Rectangular array binomial(k+3,4)*binomial(n+3,4), by antidiagonals. 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

Northwest corner:

   1,    5,   15,   35,   70

   5,   25,   75,  175,  350

  15,   75,  225,  525, 1050

  35,  175,  425, 1225, 2450

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 *)

CROSSREFS

Cf. A144112.

Row 1 = Column 1 = A000332.

Sequence in context: A104551 A100746 A185785 * A050341 A140360 A178821

Adjacent sequences:  A185902 A185903 A185904 * A185906 A185907 A185908

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 06 2011

STATUS

approved

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Last modified February 19 06:46 EST 2018. Contains 299330 sequences. (Running on oeis4.)