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

%I

%S 1,5,5,15,25,15,35,75,75,35,70,175,225,175,70,126,350,525,525,350,126,

%T 210,630,1050,1225,1050,630,210,330,1050,1890,2450,2450,1890,1050,330,

%U 495,1650,3150,4410,4900,4410,3150,1650,495,715,2475,4950,7350,8820,8820,7350,4950,2475,715,1001,3575,7425,11550

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

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

%H G. C. Greubel, <a href="/A185905/b185905.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%e Northwest corner:

%e 1, 5, 15, 35, 70

%e 5, 25, 75, 175, 350

%e 15, 75, 225, 525, 1050

%e 35, 175, 425, 1225, 2450

%t 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 *)

%Y Cf. A144112.

%Y Row 1 = Column 1 = A000332.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 06 2011

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Last modified February 22 18:05 EST 2019. Contains 320400 sequences. (Running on oeis4.)