A379086
a(n) = Sum_{k=0..floor(n/2)} binomial(3*n+k-1,k) * binomial(3*n+k,n-2*k).
Original entry on oeis.org
1, 3, 21, 174, 1509, 13443, 121962, 1120899, 10401021, 97230090, 914283621, 8638552464, 81945757734, 779949538176, 7444735446813, 71237074583589, 683125330952205, 6563268117869076, 63164380112090814, 608805362150884731, 5875874727915635409, 56780302474503539427, 549294315060885105744
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*n+k-1, k)*binomial(3*n+k, n-2*k));
A379090
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x^3*A(x)^10).
Original entry on oeis.org
1, 1, 3, 13, 69, 409, 2578, 16883, 113606, 780710, 5457275, 38687680, 277511415, 2010540125, 14690727157, 108136401031, 801111528944, 5968615651663, 44692765261977, 336164201398198, 2538745667960316, 19242953564513454, 146340183680256968, 1116267947369766774
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(3*n+k+1, k)*binomial(3*n+k+1, n-3*k)/(3*n+k+1));
A379083
Expansion of (1/x) * Series_Reversion( x * (1/(1 + x) - x^3)^3 ).
Original entry on oeis.org
1, 3, 12, 58, 321, 1941, 12405, 82188, 558567, 3870694, 27245268, 194269872, 1400352702, 10187886330, 74710928103, 551676261727, 4098401671788, 30610414484517, 229717037309281, 1731295701244008, 13098454442320593, 99444838611953627, 757393732018935552, 5785220154325055826
Offset: 0
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a(n) = 3*sum(k=0, n\3, binomial(3*n+k+3, k)*binomial(3*n+k+3, n-3*k)/(3*n+k+3));
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