A379084
a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(2*n+k,n-2*k).
Original entry on oeis.org
1, 2, 10, 62, 394, 2562, 16966, 113794, 770458, 5254658, 36046470, 248449104, 1719175846, 11935608518, 83100064834, 579994824042, 4056746450106, 28428354905268, 199550820571858, 1402832286126650, 9875127071717694, 69599814539512900, 491081313666879968, 3468458841769675496
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(2*n+k-1, k)*binomial(2*n+k, n-2*k));
A379089
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2) * (1 + x^3*A(x)^7).
Original entry on oeis.org
1, 1, 2, 6, 24, 108, 503, 2385, 11537, 56992, 286769, 1464317, 7564803, 39457205, 207500615, 1099066181, 5858206629, 31399478619, 169132215962, 915057263082, 4970445985138, 27095859218337, 148193424618950, 812923791698402, 4471543767583949, 24657936277287687
Offset: 0
-
a(n) = sum(k=0, n\3, binomial(2*n+k+1, k)*binomial(2*n+k+1, n-3*k)/(2*n+k+1));
A379082
Expansion of (1/x) * Series_Reversion( x * (1/(1 + x) - x^3)^2 ).
Original entry on oeis.org
1, 2, 5, 16, 64, 288, 1354, 6496, 31728, 157818, 798098, 4091712, 21211165, 110969430, 585116287, 3106334810, 16590881379, 89085610328, 480627775528, 2604103448334, 14163573236255, 77302955664902, 423245859576867, 2324046398587426, 12795255089638583, 70617777139027756
Offset: 0
-
a(n) = 2*sum(k=0, n\3, binomial(2*n+k+2, k)*binomial(2*n+k+2, n-3*k)/(2*n+k+2));
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