A364864
G.f. A(x) satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 2, 4, 6, -1, -58, -304, -1090, -2876, -4216, 9244, 106746, 529962, 1874628, 4669760, 4309742, -35179252, -277928680, -1269921008, -4214431912, -9197175241, 30113526, 128659598896, 822227670866, 3453484223084, 10519017940952, 18490932535144
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(3*n+k+1, n)/(3*n+k+1));
A364866
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^5).
Original entry on oeis.org
1, 1, 4, 21, 124, 781, 5120, 34474, 236492, 1644222, 11543644, 81623504, 580104672, 4137414963, 29574658416, 211639869236, 1514729242092, 10832683182538, 77342204972120, 550791674067623, 3908735530965604, 27612614422978557, 193943797650498016
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(5*n+k+1, n)/(5*n+k+1));
A378920
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 5, 38, 339, 3308, 34191, 367844, 4076112, 46204209, 533239820, 6244542391, 74016115926, 886276231388, 10704869669941, 130271156244371, 1595708949486866, 19658780721376791, 243429900033986385, 3028086095940468087, 37821457123957529163, 474145963420441744445
Offset: 0
-
a(n, r=1, s=-1, t=6, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A365226
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 + x*A(x)^6).
Original entry on oeis.org
1, 1, 4, 20, 107, 577, 3010, 14429, 56640, 98020, -1297568, -21901213, -232421636, -2081040375, -16862259358, -126674303915, -887771735205, -5768588276072, -33971373570320, -170393703586467, -576946353425125, 1101490168511323, 47657979846612682
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n-k+1, k)*binomial(n-1, n-k)/(6*n-k+1));
A378919
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)).
Original entry on oeis.org
1, 1, 5, 39, 355, 3532, 37206, 407861, 4604493, 53169811, 625067441, 7456004083, 90015754691, 1097834790182, 13505674728174, 167395320811562, 2088350145491232, 26203315734195937, 330460721192844017, 4186559092558049570, 53255890990455126082, 679954025388880445771
Offset: 0
-
a(n, r=1, s=-1, t=6, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
Showing 1-5 of 5 results.
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