A126446
Column 0 of triangle A126445; a(n) = binomial( binomial(n+2,3), n).
Original entry on oeis.org
1, 1, 6, 120, 4845, 324632, 32468436, 4529365776, 840261910995, 200063149171380, 59473554359599446, 21592914273609648996, 9403538945961296957821, 4838670732821812768919800, 2904538537066424425438417800
Offset: 0
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[(Binomial(Binomial(n+3, n), n+1)): n in [-1..20]]; // Vincenzo Librandi, Mar 04 2018
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Table[Binomial[n (n + 1) (n + 2) / 3!, n], {n, 0, 20}] (* Vincenzo Librandi, Mar 04 2018 *)
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a(n)=binomial(n*(n+1)*(n+2)/3!, n)
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[(binomial(binomial(n+3,n),n+1)) for n in range(-1, 12)] # Zerinvary Lajos, Nov 30 2009
A126457
Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 3, n-k) for n>=k>=0.
Original entry on oeis.org
1, 4, 1, 21, 6, 1, 286, 66, 9, 1, 8855, 1540, 171, 13, 1, 501942, 66045, 5984, 378, 18, 1, 45057474, 4582116, 341055, 18424, 741, 24, 1, 5843355957, 470155077, 29034396, 1353275, 47905, 1326, 31, 1, 1029873432159, 66983637864, 3470108187, 140364532
Offset: 0
Formula: T(n,k) = C( C(n+2,3) - C(k+2,3) + 3, n-k) is illustrated by:
T(n=4,k=1) = C( C(6,3) - C(3,3) + 3, n-k) = C(22,3) = 1540;
T(n=4,k=2) = C( C(6,3) - C(4,3) + 3, n-k) = C(19,2) = 171;
T(n=5,k=2) = C( C(7,3) - C(4,3) + 3, n-k) = C(34,3) = 5984.
Triangle begins:
1;
4, 1;
21, 6, 1;
286, 66, 9, 1;
8855, 1540, 171, 13, 1;
501942, 66045, 5984, 378, 18, 1;
45057474, 4582116, 341055, 18424, 741, 24, 1;
5843355957, 470155077, 29034396, 1353275, 47905, 1326, 31, 1; ...
A126451
Column 0 of triangle A126450; a(n) = C( C(n+2,3) + 1, n).
Original entry on oeis.org
1, 2, 10, 165, 5985, 376992, 36288252, 4935847320, 899749479915, 211531737340440, 62292206224983306, 22453501436688294427, 9723205992282927449305, 4980663327690172963041600, 2978877731799385928100461400, 2057145404864429538334152506640
Offset: 0
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[Binomial(Binomial(n+2,3)+1,n): n in [0..20]]; // Vincenzo Librandi, Mar 10 2014
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Table[Binomial[Binomial[n+2,3]+1,n],{n,0,20}] (* Harvey P. Dale, Mar 08 2014 *)
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a(n)=binomial(n*(n+1)*(n+2)/3!+1, n)
A126455
Column 0 of triangle A126454; a(n) = C( C(n+2,3) + 2, n).
Original entry on oeis.org
1, 3, 15, 220, 7315, 435897, 40475358, 5373200880, 962889794295, 223581013518060, 65230517839369311, 23345156728397937888, 10052806195411162278095, 5126493560257678027274800
Offset: 0
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Table[Binomial[Binomial[n+2,3]+2,n],{n,0,20}] (* Harvey P. Dale, Dec 08 2018 *)
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a(n)=binomial(n*(n+1)*(n+2)/3!+2, n)
A126459
Column 1 of triangle A126457; a(n) = C( C(n+3,3) + 2, n).
Original entry on oeis.org
1, 6, 66, 1540, 66045, 4582116, 470155077, 66983637864, 12655529067060, 3062465626261470, 923729223066105456, 339813167168828020668, 149762733221010818774320, 77904783726874238769542600
Offset: 0
Showing 1-5 of 5 results.
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