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));
A365218
G.f. satisfies A(x) = 1 + x*A(x)^6 / (1 + x*A(x)^6).
Original entry on oeis.org
1, 1, 5, 34, 265, 2232, 19766, 181300, 1706737, 16392049, 159959240, 1581278838, 15800619070, 159321921844, 1618981274136, 16562211506496, 170426473666497, 1762771226922775, 18316562635133813, 191104193378725552, 2001224271292820200
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*n+1, k)*binomial(n-1, n-k))/(6*n+1);
A364865
G.f. satisfies A(x) = 1 + x*A(x)^4 / (1 + x*A(x)^4).
Original entry on oeis.org
1, 1, 3, 11, 43, 170, 657, 2392, 7675, 17603, -11898, -529678, -4783303, -33099464, -201744488, -1130700432, -5917753701, -28985131575, -131668554663, -540199800203, -1862208441834, -4014999475540, 10784817197302, 222255824910088, 1973412557775753
Offset: 0
-
a(n) = sum(k=0, n, (-1)^k*2^(n-k)*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1));
A378892
G.f. A(x) satisfies A(x) = 1 + x*A(x)^6/(1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 5, 37, 322, 3067, 30951, 325171, 3519038, 38959997, 439177850, 5023590609, 58163050071, 680308820750, 8026782091957, 95419476630100, 1141762194395927, 13740910664096101, 166216043531507231, 2019807368837970964, 24644779751103948475, 301818330734940817283
Offset: 0
-
a(n, r=1, s=-1, t=6, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A365223
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 + x*A(x)^4).
Original entry on oeis.org
1, 1, 2, 3, -3, -50, -244, -714, -530, 8522, 63548, 259473, 535647, -1321437, -19094684, -103022071, -322370363, -142186810, 5537336460, 41081448638, 170484444654, 332739198585, -1241023311708, -15677607031084, -83737193010368, -255608722098225, -12706843586158
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(4*n-k+1, k)*binomial(n-1, n-k)/(4*n-k+1));
Showing 1-5 of 5 results.
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