A371538
G.f. A(x) satisfies A(x) = (1 + x*A(x)^2 / (1+x))^3.
Original entry on oeis.org
1, 3, 18, 151, 1440, 14835, 160793, 1806849, 20859129, 245905348, 2947869600, 35825319390, 440372147956, 5465555197818, 68396554601013, 862066323857486, 10933638171672105, 139439595024315675, 1787056241039876890, 23003636498360053905, 297283046361025602900
Offset: 0
-
a(n) = 3*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+3, k)/(6*k+3));
A371537
G.f. A(x) satisfies A(x) = (1 + x*A(x)^3 / (1+x))^2.
Original entry on oeis.org
1, 2, 11, 90, 845, 8620, 92792, 1037474, 11930952, 140223730, 1676824810, 20336742860, 249554057158, 3092735367966, 38653949888993, 486656046354650, 6166315484899445, 78573243500307870, 1006223574171080479, 12943581721362983708, 167170200918998754129
Offset: 0
-
a(n) = 2*sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+2, k)/(6*k+2));
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));
A371541
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^6.
Original entry on oeis.org
1, 6, 45, 410, 4110, 43746, 485237, 5547396, 64901670, 773296320, 9350929395, 114464359296, 1415620823147, 17661466502796, 222017667461685, 2809362871991380, 35755481454362355, 457410181217186886, 5878378983480722222, 75856853080508789406
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+6, k)/(k+1));
Showing 1-4 of 4 results.