A385319
a(n) = Sum_{k=0..n} 2^k * binomial(2*n,k) * binomial(2*n-k-1,n-k).
Original entry on oeis.org
1, 5, 43, 422, 4387, 47090, 515854, 5731052, 64330531, 727812026, 8285505178, 94798502804, 1089146648206, 12556967516852, 145201851788092, 1683334752235352, 19558532125813027, 227694254392461962, 2655343386035416162, 31014205667706302852, 362746369474101224602
Offset: 0
-
Table[Sum[3^k*(-1)^(n-k)*Binomial[2*n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 31 2025 *)
-
a(n) = sum(k=0, n, 2^k*binomial(2*n,k)*binomial(2*n-k-1, n-k));
A386723
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / (1+2*x)^4 ).
Original entry on oeis.org
1, 11, 175, 3275, 67156, 1460237, 33073930, 771961835, 18437940220, 448483875596, 11071403236807, 276675755470349, 6985664542196380, 177932236341440270, 4566561255466298500, 117974930924420353835, 3065563791639454312492, 80069021664742889373380
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)^3/(1+2*x)^4)/x)
-
a(n) = sum(k=0, n, 2^k*binomial(4*(n+1), k)*binomial(4*n-k+2, n-k))/(n+1);
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);
A371392
Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+2*x)^3 ).
Original entry on oeis.org
1, 7, 68, 769, 9492, 124014, 1686120, 23610565, 338200148, 4932348226, 72993007672, 1093371638954, 16545598769416, 252567107648604, 3884497559034192, 60136704175071789, 936373570430169300, 14654788984834217850, 230405413840884827160, 3637362857723455772670
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+2*x)^3)/x)
-
a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
A386772
Expansion of (1/x) * Series_Reversion( x * (1-3*x) / (1+2*x)^2 ).
Original entry on oeis.org
1, 7, 74, 943, 13326, 200982, 3169524, 51633343, 862145126, 14677296082, 253802667724, 4445613370118, 78712814985676, 1406483499289932, 25330499214488424, 459331317209458143, 8379478714912128726, 153679237018626276282, 2831839422052964444124
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)/(1+2*x)^2)/x)
-
a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(2*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
Showing 1-5 of 5 results.