A371521
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^6.
Original entry on oeis.org
1, 6, 57, 614, 7158, 88002, 1123689, 14760024, 198172050, 2707560544, 37522666803, 526190125308, 7452866846847, 106465245105972, 1532129408941797, 22191180837313808, 323243244688652943, 4732225866305323686, 69591395772704207770, 1027547992261749954798
Offset: 0
-
a(n) = 6*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+5, k)/(5*k+6));
A371523
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1-x))^2.
Original entry on oeis.org
1, 2, 15, 142, 1533, 17924, 220936, 2827218, 37202580, 500228562, 6842899886, 94931338876, 1332438761910, 18887047322030, 269986427261981, 3887654399820062, 56337997080499605, 821021578186212094, 12024687038651388155, 176900548019426869808, 2612917215947948178941
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+1, k)/(5*k+2));
A371519
G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1-x))^5.
Original entry on oeis.org
1, 5, 45, 470, 5375, 65231, 825225, 10764185, 143739440, 1955340360, 27001732972, 377530388235, 5333865386885, 76031188364860, 1092117166466660, 15792298241897649, 229704197116753825, 3358528175751886765, 49333470827844265285, 727680248026484478405
Offset: 0
-
a(n) = sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));
A371522
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1-x))^3.
Original entry on oeis.org
1, 3, 24, 235, 2586, 30603, 380359, 4896753, 64731747, 873539236, 11984536632, 166661420814, 2343950447112, 33282048811530, 476462982915993, 6869620848003570, 99663539644072305, 1453861111238442363, 21312207036239313936, 313783619269186619589
Offset: 0
-
a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(6*k+2, k)/(5*k+3));
A371539
G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/2) / (1+x))^4.
Original entry on oeis.org
1, 4, 26, 224, 2171, 22600, 246754, 2787856, 32318849, 382266056, 4594893684, 55966343520, 689245218880, 8568130064280, 107371481352870, 1354944741505580, 17203182641794020, 219604431213873060, 2816826935574781930, 36286757255072528360, 469266638574298431490
Offset: 0
-
a(n) = 4*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+4, k)/(6*k+4));
A370695
G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/4) / (1-x))^4.
Original entry on oeis.org
1, 4, 22, 128, 777, 4872, 31330, 205560, 1370868, 9266104, 63343006, 437183260, 3042337215, 21323543252, 150395596016, 1066637271424, 7602188660799, 54422262148632, 391146728466980, 2821396586367568, 20417766975784066, 148200184917042112
Offset: 0
-
A370695 := proc(n)
4*add(binomial(n-1,n-k)*binomial(3*k+4,k)/(3*k+4),k=0..n) ;
end proc:
seq(A370695(n),n=0..80) ; #R. J. Mathar, Oct 24 2024
-
a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+4, k)/(3*k+4));
Showing 1-6 of 6 results.