A386837
a(n) = Sum_{k=0..n} binomial(4*n+2,k) * binomial(4*n-k-1,n-k).
Original entry on oeis.org
1, 9, 126, 1978, 32703, 556887, 9665476, 170006256, 3019802253, 54047520709, 973141183002, 17607177876438, 319855973830251, 5830329608105763, 106583422441886592, 1953315343946213804, 35875864591309216089, 660185366847433991025, 12169379986275311820790
Offset: 0
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a(n) = sum(k=0, n, binomial(4*n+2, k)*binomial(4*n-k-1, n-k));
A386833
a(n) = Sum_{k=0..n} binomial(3*n+1,k) * binomial(3*n-k-1,n-k).
Original entry on oeis.org
1, 6, 59, 656, 7701, 93210, 1150495, 14395428, 181936169, 2317140014, 29691138099, 382334271544, 4943464235069, 64137141682242, 834561532624967, 10886878474010700, 142332442919829585, 1864423992564121686, 24464149489904517211, 321499324010641490016, 4230840338116037836901
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+1, k)*binomial(3*n-k-1, n-k));
A386938
a(n) = Sum_{k=0..n} binomial(4*n+1,k) * binomial(2*n-k-1,n-k).
Original entry on oeis.org
1, 6, 57, 608, 6835, 79170, 934892, 11189568, 135263799, 1647649850, 20191754297, 248664799344, 3074813151956, 38151145101048, 474747568376520, 5922579575399680, 74047774139941503, 927579860291591226, 11639480787978105179, 146278009406326705600, 1840856649159814801515
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*n+1, k)*binomial(2*n-k-1, n-k));
A386939
a(n) = Sum_{k=0..n} binomial(4*n+1,k) * binomial(3*n-k-1,n-k).
Original entry on oeis.org
1, 7, 82, 1083, 15086, 216566, 3169636, 47020371, 704497750, 10636206306, 161553957500, 2465911305182, 37791965926092, 581171323026508, 8963417696439752, 138590900605115779, 2147571141595692390, 33342454213792397930, 518548824827926272268, 8076888443386745743530
Offset: 0
-
[&+[Binomial(4*n+1,k) * Binomial(3*n-k-1,n-k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 03 2025
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Table[Sum[Binomial[4*n+1, k]*Binomial[3*n-k-1,n-k],{k,0,n}],{n,0,30}] (* Vincenzo Librandi, Sep 03 2025 *)
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a(n) = sum(k=0, n, binomial(4*n+1, k)*binomial(3*n-k-1, n-k));
Showing 1-4 of 4 results.