A386719
a(n) = Sum_{k=0..n} 2^k * binomial(4*n,k) * binomial(4*n-k-1,n-k).
Original entry on oeis.org
1, 11, 229, 5381, 133333, 3404156, 88600483, 2337160718, 62263902037, 1671407550260, 45137852641204, 1224954657942125, 33377579214681619, 912572183952374996, 25023054179816358034, 687862647149533181036, 18950129471489195622229, 523067259899842250453060
Offset: 0
-
Table[Sum[3^k*(-1)^(n-k)*Binomial[4*n, k], {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Jul 31 2025 *)
-
a(n) = sum(k=0, n, 2^k*binomial(4*n, k)*binomial(4*n-k-1, n-k));
A386722
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+2*x)^3 ).
Original entry on oeis.org
1, 8, 91, 1214, 17731, 274526, 4426948, 73561238, 1250803171, 21659155028, 380638861219, 6771681469952, 121716110229364, 2207040281944856, 40323735229993336, 741613603443652214, 13718779315483616227, 255086483631977702096, 4764893748897482791633, 89373590789286772582334
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+2*x)^3)/x)
-
a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(3*n-k+1, n-k))/(n+1);
A385475
Expansion of (1/x) * Series_Reversion( x * (1-2*x)^3 / (1+x)^4 ).
Original entry on oeis.org
1, 10, 154, 2836, 57601, 1244584, 28063288, 652821724, 15551944804, 377503375150, 9303441938506, 232168129150420, 5854967533764766, 148981015820615968, 3820184959840942564, 98616983735455104412, 2560818171703792341484, 66845502538144505160040
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-2*x)^3/(1+x)^4)/x)
-
a(n) = sum(k=0, n, 2^(n-k)*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
A386774
Expansion of (1/x) * Series_Reversion( x * (1-3*x)^3 / (1+2*x)^4 ).
Original entry on oeis.org
1, 17, 439, 13513, 458196, 16518407, 621247194, 24099952473, 957294067516, 38741943503972, 1591753835634799, 66219447135668383, 2783826043226606236, 118078452737821009962, 5047034289902290964004, 217173909723115943823993, 9400092428228971114597356
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)^3/(1+2*x)^4)/x)
-
a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
Showing 1-4 of 4 results.