A114252
a(n) = C(4+2*n,4+n)*C(9+2*n,0+n).
Original entry on oeis.org
1, 66, 2184, 54600, 1178100, 23279256, 434546112, 7801876368, 136246002750, 2331320491500, 39283977292560, 654191853260400, 10794165578796600, 176805993477330000, 2879098129810080000, 46660583690455363200, 753276797952788769660, 12121801610494996922040
Offset: 0
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Table[Binomial[4+2n,4+n]Binomial[9+2n,n],{n,0,20}] (* Harvey P. Dale, Aug 30 2015 *)
A348539
Triangle T(n, m) = binomial(n+2, m)*binomial(n+2, n-m), read by rows.
Original entry on oeis.org
1, 3, 3, 6, 16, 6, 10, 50, 50, 10, 15, 120, 225, 120, 15, 21, 245, 735, 735, 245, 21, 28, 448, 1960, 3136, 1960, 448, 28, 36, 756, 4536, 10584, 10584, 4536, 756, 36, 45, 1200, 9450, 30240, 44100, 30240, 9450, 1200, 45, 55, 1815, 18150, 76230, 152460, 152460, 76230, 18150, 1815, 55
Offset: 0
Triangle starts:
[0] 1;
[1] 3, 3;
[2] 6, 16, 6;
[3] 10, 50, 50, 10;
[4] 15, 120, 225, 120, 15;
[5] 21, 245, 735, 735, 245, 21;
[6] 28, 448, 1960, 3136, 1960, 448, 28.
...
Taylor series: 1 + 3*x*(y + 1) + 2*x^2*(3*y^2 + 8*y + 3) + 10*x^3*(y^3 + 5*y^2 + 5*y + 1) + 15*x^4 (y^4 + 8*y^3 + 15*y^2 + 8*y + 1) + O(x^5)
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T := (n, k) -> binomial(n+2, k) * binomial(n+2, n-k):
for n from 0 to 9 do seq(T(n, k), k = 0..n) od; # Peter Luschny, Oct 22 2021
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T[n_, m_] := Binomial[n + 2, m] * Binomial[n + 2, n - m]; Table[T[n, m], {n, 0, 9}, {m, 0, n}] // Flatten (* Amiram Eldar, Oct 22 2021 *)
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T(n,m):=binomial(n+2,m)*binomial(n+2,n-m);