A379087
a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+k-1,k) * binomial(3*n+k,n-3*k).
Original entry on oeis.org
1, 3, 15, 93, 651, 4803, 36177, 275208, 2108091, 16243671, 125817345, 978933354, 7646000421, 59915086026, 470820659940, 3708756501018, 29276677544619, 231540519752376, 1834228504348863, 14552075416977531, 115605043235217081, 919503729585453147
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(3*n+k-1, k)*binomial(3*n+k, n-3*k));
A379088
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)^7).
Original entry on oeis.org
1, 1, 4, 23, 153, 1106, 8443, 66977, 546688, 4561527, 38732871, 333607557, 2907549308, 25594629702, 227233349522, 2032335895221, 18294192036084, 165612099597170, 1506797883831078, 13771122728779086, 126368176338669841, 1163834520126009000, 10754353177914306483
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(3*n+k+1, k)*binomial(3*n+k+1, n-2*k)/(3*n+k+1));
A379081
Expansion of (1/x) * Series_Reversion( x * (1/(1 + x) - x^2)^3 ).
Original entry on oeis.org
1, 3, 15, 94, 657, 4905, 38299, 308928, 2554092, 21528728, 184318944, 1598427531, 14011401996, 123946608699, 1105090991634, 9920335032821, 89589290332200, 813367589142888, 7419376746340780, 67965042988027335, 624971955439306953, 5766825797557702751, 53380176096582823851
Offset: 0
-
a(n) = 3*sum(k=0, n\2, binomial(3*n+k+3, k)*binomial(3*n+k+3, n-2*k)/(3*n+k+3));
Showing 1-3 of 3 results.