A371826
a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-k,n-2*k).
Original entry on oeis.org
1, 2, 8, 35, 170, 872, 4740, 26994, 161006, 1001009, 6476976, 43480373, 302250196, 2170406149, 16070240276, 122453910495, 958755921686, 7701233828576, 63381318474768, 533793776053926, 4595440308780620, 40400161269188412, 362367733795887848
Offset: 0
A371825
a(n) = Sum_{k=0..n} n^k * binomial(2*n,n-k).
Original entry on oeis.org
1, 3, 18, 146, 1510, 19302, 296520, 5339924, 110447046, 2581169510, 67274981356, 1934941601628, 60878718397276, 2080009638726684, 76694241037743300, 3035502492679964520, 128364744764608411718, 5776084128332328033798, 275565308510875579650348
Offset: 0
A371837
a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-3*k-1,n-3*k).
Original entry on oeis.org
1, 1, 3, 13, 51, 201, 834, 3529, 15075, 65431, 288278, 1285263, 5799470, 26492103, 122432628, 572291385, 2705760291, 12937116213, 62542367166, 305668511259, 1510080076410, 7539381024297, 38034307340076, 193835252945487, 997724306958606, 5185731234177001
Offset: 0
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Join[{1}, Table[Sum[n^k*Binomial[2*n-3*k-1,n-1], {k, 0, n/3}], {n, 1, 25}]] (* Vaclav Kotesovec, Apr 08 2024 *)
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a(n) = sum(k=0, n\3, n^k*binomial(2*n-3*k-1, n-3*k));
Showing 1-3 of 3 results.