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
-
[(Binomial(Binomial(n+3, n), n+1)): n in [-1..20]]; // Vincenzo Librandi, Mar 04 2018
-
Table[Binomial[n (n + 1) (n + 2) / 3!, n], {n, 0, 20}] (* Vincenzo Librandi, Mar 04 2018 *)
-
a(n)=binomial(n*(n+1)*(n+2)/3!, n)
-
[(binomial(binomial(n+3,n),n+1)) for n in range(-1, 12)] # Zerinvary Lajos, Nov 30 2009
A126454
Triangle, read by rows, where T(n,k) = C( C(n+2,3) - C(k+2,3) + 2, n-k) for n>=k>=0.
Original entry on oeis.org
1, 3, 1, 15, 5, 1, 220, 55, 8, 1, 7315, 1330, 153, 12, 1, 435897, 58905, 5456, 351, 17, 1, 40475358, 4187106, 316251, 17296, 703, 23, 1, 5373200880, 437353560, 27285336, 1282975, 45760, 1275, 30, 1, 962889794295, 63140314380, 3295144749, 134153712
Offset: 0
Formula: T(n,k) = C( C(n+2,3) - C(k+2,3) + 2, n-k) is illustrated by:
T(n=4,k=1) = C( C(6,3) - C(3,3) + 2, n-k) = C(21,3) = 1330;
T(n=4,k=2) = C( C(6,3) - C(4,3) + 2, n-k) = C(18,2) = 153;
T(n=5,k=2) = C( C(7,3) - C(4,3) + 2, n-k) = C(33,3) = 5456.
Triangle begins:
1;
3, 1;
15, 5, 1;
220, 55, 8, 1;
7315, 1330, 153, 12, 1;
435897, 58905, 5456, 351, 17, 1;
40475358, 4187106, 316251, 17296, 703, 23, 1;
5373200880, 437353560, 27285336, 1282975, 45760, 1275, 30, 1; ...
-
Table[Binomial[Binomial[n+2,3]-Binomial[k+2,3]+2,n-k],{n,0,10},{k,0,n}]// Flatten (* Harvey P. Dale, Dec 17 2020 *)
-
T(n,k)=binomial(n*(n+1)*(n+2)/3!-k*(k+1)*(k+2)/3!+2, n-k)
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
-
[Binomial(Binomial(n+2,3)+1,n): n in [0..20]]; // Vincenzo Librandi, Mar 10 2014
-
Table[Binomial[Binomial[n+2,3]+1,n],{n,0,20}] (* Harvey P. Dale, Mar 08 2014 *)
-
a(n)=binomial(n*(n+1)*(n+2)/3!+1, n)
A126456
Column 1 of triangle A126454; a(n) = C( C(n+3,3) + 1, n).
Original entry on oeis.org
1, 5, 55, 1330, 58905, 4187106, 437353560, 63140314380, 12049276177620, 2938311614386005, 891655291709643461, 329600203128234828790, 145830232567505064233200, 76102715775896720790887700
Offset: 0
-
Table[Binomial[Binomial[n+3,3]+1,n],{n,0,20}] (* Harvey P. Dale, Feb 03 2015 *)
-
a(n)=binomial((n+1)*(n+2)*(n+3)/3!+1, n)
A126458
Column 0 of triangle A126457; a(n) = C( C(n+2,3) + 3, n).
Original entry on oeis.org
1, 4, 21, 286, 8855, 501942, 45057474, 5843355957, 1029873432159, 236236542585120, 68292983465630781, 24268885951464043344, 10392619362579990298763, 5276256293478688846049120
Offset: 0
Showing 1-5 of 5 results.
Comments