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));
A371540
G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1+x))^5.
Original entry on oeis.org
1, 5, 35, 310, 3055, 32151, 353755, 4019825, 46808750, 555621400, 6698027100, 81779512155, 1009194553315, 12567338972700, 157725047958100, 1992990741398625, 25333585976926275, 323725357496659565, 4156196637610760235, 53585106340408250725, 693491493195479127175
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+4, k)/(k+1));
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));
A371542
G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^3.
Original entry on oeis.org
1, 3, 9, 34, 141, 621, 2849, 13467, 65127, 320686, 1602294, 8103087, 41397186, 213331026, 1107604764, 5788249329, 30422897664, 160717169622, 852894534042, 4544635033164, 24305345593290, 130423538829518, 701994030831654, 3788979493701069, 20503322609731348
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(3*k+3, k)/(k+1));
Showing 1-5 of 5 results.