A364748
G.f. A(x) satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)).
Original entry on oeis.org
1, 1, 6, 47, 424, 4159, 43097, 464197, 5145475, 58313310, 672598269, 7869856070, 93183973405, 1114471042413, 13443614108307, 163372291277764, 1998239045199623, 24580340878055298, 303893356012560280, 3774099648814193998, 47061518776483143441
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(5*n-4*k, n-1-k))/n);
-
a(n, r=1, s=1, t=5, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r)); \\ Seiichi Manyama, Dec 05 2024
A365186
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 6, 47, 428, 4241, 44407, 483358, 5414618, 62014112, 722870120, 8547768832, 102284029963, 1236274747490, 15070955944288, 185089043535730, 2287843817573898, 28440852786725695, 355345599519983962, 4459821165693379625, 56200963128262312342
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(k, n-k)/(2*n+3*k+1));
A365193
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^3).
Original entry on oeis.org
1, 1, 6, 49, 463, 4760, 51702, 583712, 6781774, 80555066, 973813974, 11941861079, 148191437719, 1857464450449, 23481830726334, 299056887494427, 3833349330581255, 49416395972195630, 640256115370243620, 8332835556325119938, 108890550249605779116
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+2*k+1, k)*binomial(n-1, n-k)/(3*n+2*k+1));
A365194
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^6).
Original entry on oeis.org
1, 1, 6, 52, 529, 5889, 69462, 853013, 10791018, 139659604, 1840435530, 24611295075, 333132371248, 4555465710569, 62839303262352, 873363902976309, 12218178082489873, 171918448407833112, 2431415226089290680, 34544425914499450493, 492807213597429920649
Offset: 0
-
a(n) = sum(k=0, n, binomial(6*n-k+1, k)*binomial(n-1, n-k)/(6*n-k+1));
A371581
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) / (1 - x*A(x)) )^2.
Original entry on oeis.org
1, 2, 13, 108, 1018, 10352, 110724, 1227752, 13986369, 162708728, 1924866345, 23085868814, 280060995369, 3430479393210, 42369377446083, 527064922683286, 6597825455023465, 83050276697808472, 1050551595788997356, 13347641275527720048, 170259412138463630535
Offset: 0
-
a(n, r=2, s=1, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
A378685
G.f. A(x) satisfies A(x) = 1 + x*A(x)^7/(1 - x*A(x)^3).
Original entry on oeis.org
1, 1, 8, 88, 1126, 15716, 232069, 3564835, 56382489, 912031280, 15018257510, 250913307393, 4242722219425, 72470224174650, 1248608968982903, 21673752440979879, 378677335852165297, 6654158090059397480, 117523324766568499072, 2085095374834405245007
Offset: 0
-
a(n, r=1, s=1, t=7, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
A371889
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, 2, 2, -1, -4, 7, 33, -5, -200, -151, 1185, 2202, -6069, -21799, 21791, 182718, 26520, -1349611, -1613331, 8674338, 21651795, -44750412, -217666394, 121538304, 1859974399, 1023915107, -13828122997, -23155237537, 86925632115, 282182920662
Offset: 0
-
a(n) = if(n==0, 1, sum(k=0, n, binomial(n, k)*binomial(n-3*k, n-k-1))/n);
Showing 1-7 of 7 results.