A364759
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)).
Original entry on oeis.org
1, 1, 4, 25, 182, 1447, 12175, 106575, 960579, 8854622, 83089537, 791063172, 7622317663, 74191096721, 728389554533, 7204640725610, 71727367291455, 718195853746770, 7227785937663908, 73069500402699226, 741712341691454837, 7556704348506425398
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(5*n-4*k, n-1-k))/n);
A378889
G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(4/3)/(1 + x*A(x)^(1/3)) )^3.
Original entry on oeis.org
1, 3, 12, 61, 348, 2127, 13617, 90132, 611802, 4235405, 29788821, 212255520, 1528928674, 11115361491, 81452537253, 601004875689, 4461440570523, 33295962947925, 249673885001674, 1880204670772221, 14213624028779964, 107823953314047139, 820541644515512502
Offset: 0
-
a(n, r=3, s=-1, t=4, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A365224
G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^5).
Original entry on oeis.org
1, 1, 3, 10, 30, 56, -167, -2813, -21515, -126135, -601812, -2179039, -3455504, 32238155, 430944400, 3334419890, 20083350422, 97094186751, 338485665435, 274332822425, -8491831747320, -97735154210032, -732963337489636, -4341176221239330
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(5*n-k+1, k)*binomial(n-1, n-k)/(5*n-k+1));
A378919
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)).
Original entry on oeis.org
1, 1, 5, 39, 355, 3532, 37206, 407861, 4604493, 53169811, 625067441, 7456004083, 90015754691, 1097834790182, 13505674728174, 167395320811562, 2088350145491232, 26203315734195937, 330460721192844017, 4186559092558049570, 53255890990455126082, 679954025388880445771
Offset: 0
-
a(n, r=1, s=-1, t=6, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A377705
G.f. A(x) satisfies A(x) = 1 + x/A(x)^2 * (1 - A(x) + A(x)^3).
Original entry on oeis.org
1, 1, 0, 2, -3, 12, -35, 121, -413, 1464, -5265, 19249, -71236, 266443, -1005511, 3824055, -14641264, 56389272, -218315173, 849170605, -3316817080, 13004273475, -51160638706, 201901154910, -799059730844, 3170706566751, -12611882813645, 50277271079611
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n, (-1)^k*binomial(n, k)*binomial(n-3*k, n-k-1))/n);
Showing 1-5 of 5 results.