A366431
G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^(5/2).
Original entry on oeis.org
1, 1, 5, 25, 135, 775, 4651, 28845, 183450, 1190050, 7844230, 52389678, 353770190, 2411324700, 16568343325, 114639216915, 798076174113, 5586035989185, 39287407321075, 277508001643575, 1967816928168265, 14003018984540741, 99965175670335750
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k/2-1, n-k)*binomial(5*k/2, k)/(3*k/2+1));
A366432
G.f. A(x) satisfies A(x) = 1 + x * (A(x) / (1 - x))^(7/2).
Original entry on oeis.org
1, 1, 7, 49, 378, 3136, 27363, 247597, 2302511, 21872361, 211336755, 2070577285, 20522662832, 205411356794, 2073258075175, 21078157565623, 215658366319375, 2218853063356937, 22942886758494094, 238284942878492146, 2484736162773443446
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+5*k/2-1, n-k)*binomial(7*k/2, k)/(5*k/2+1));
A366434
G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^2.
Original entry on oeis.org
1, 1, -4, 16, -84, 496, -3140, 20832, -142932, 1005856, -7220100, 52657392, -389088084, 2906551440, -21914464708, 166548194240, -1274531623764, 9812792232768, -75955668337412, 590742300208848, -4614140648464980, 36178872976542768, -284664427193774916
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(3*k-1, k)*binomial(2*k, n-k)/(3*k-1));
A366435
G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^(5/2).
Original entry on oeis.org
1, 1, -5, 25, -160, 1150, -8851, 71345, -594530, 5080300, -44272760, 391961328, -3515490820, 31874449160, -291676084205, 2690284784605, -24985250240043, 233447554879855, -2192862233710505, 20696454624488125, -196168344717398010, 1866499116495323946
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(7*k/2-1, k)*binomial(5*k/2, n-k)/(7*k/2-1));
A366436
G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^3.
Original entry on oeis.org
1, 1, -6, 36, -272, 2304, -20880, 198080, -1942080, 19521792, -200101376, 2083538688, -21976624128, 234321952768, -2521446660096, 27347192389632, -298643542716416, 3280990949720064, -36238161907974144, 402146115064233984, -4481721683926056960
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(4*k-1, k)*binomial(3*k, n-k)/(4*k-1));
A366437
G.f. A(x) satisfies A(x) = 1 + x * ((1 - x) / A(x))^(7/2).
Original entry on oeis.org
1, 1, -7, 49, -427, 4165, -43435, 473977, -5344333, 61772179, -727993301, 8714701219, -105672771225, 1295237037815, -16021641194545, 199747074505773, -2507395464414008, 31664298046926328, -401994771266030880, 5127701624204157600, -65684716411944207144
Offset: 0
-
a(n) = (-1)^(n-1)*sum(k=0, n, binomial(9*k/2-1, k)*binomial(7*k/2, n-k)/(9*k/2-1));
A366495
G.f. A(x) satisfies A(x) = 1 + x*(1+x)^(3/2)*A(x)^(5/2).
Original entry on oeis.org
1, 1, 4, 16, 74, 366, 1900, 10210, 56315, 317005, 1813860, 10518652, 61684208, 365177622, 2179549853, 13100686947, 79232836206, 481821573994, 2944253855746, 18069720545174, 111333779015326, 688399685561554, 4270250156814421, 26567075153764929
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*k/2, n-k)*binomial(5*k/2, k)/(3*k/2+1));
Showing 1-7 of 7 results.