A371827
a(n) = Sum_{k=0..floor(n/3)} n^k * binomial(2*n-2*k,n-3*k).
Original entry on oeis.org
1, 2, 6, 23, 94, 392, 1680, 7387, 33110, 150905, 698996, 3287550, 15685420, 75877427, 371994692, 1847450970, 9290557158, 47291312897, 243574276884, 1268915237141, 6683909556420, 35585631836229, 191433293140656, 1040197718292138, 5707318227692796
Offset: 0
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Join[{1},Table[Sum[n^k Binomial[2n-2k,n-3k],{k,0,Floor[n/3]}],{n,30}]] (* Harvey P. Dale, Aug 10 2024 *)
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a(n) = sum(k=0, n\3, n^k*binomial(2*n-2*k, n-3*k));
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
A371836
a(n) = Sum_{k=0..floor(n/2)} n^k * binomial(2*n-2*k-1,n-2*k).
Original entry on oeis.org
1, 1, 5, 19, 91, 426, 2190, 11467, 63811, 365806, 2200978, 13677962, 88553726, 591576220, 4093814812, 29164567635, 214244414371, 1616044475734, 12523774634922, 99418836782602, 808492937082410, 6720935024074092, 57100849909374340, 495022008799053006
Offset: 0
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Join[{1}, Table[Sum[n^k*Binomial[2*n-2*k-1,n-1], {k, 0, n/2}], {n, 1, 25}]] (* Vaclav Kotesovec, Apr 08 2024 *)
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a(n) = sum(k=0, n\2, n^k*binomial(2*n-2*k-1, n-2*k));
Showing 1-3 of 3 results.