A365110
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^3.
Original entry on oeis.org
1, 1, -3, 3, 11, -54, 66, 297, -1575, 1980, 10300, -55392, 68352, 403583, -2153685, 2551845, 16999045, -89142087, 99986901, 750955382, -3850437018, 4041467331, 34310059311, -171533033904, 166630375248, 1607168518073, -7821913867611, 6950050797297
Offset: 0
-
a(n, s=3) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A365111
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^4.
Original entry on oeis.org
1, 1, -4, 6, 16, -119, 240, 630, -5656, 13044, 31568, -323102, 816172, 1772553, -20373748, 55339784, 105991968, -1366239119, 3950894080, 6570520544, -95534073488, 292319792622, 414994066768, -6884779019086, 22198354364212, 26341578132594, -507524582140912
Offset: 0
-
a(n, s=4) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A365109
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^2.
Original entry on oeis.org
1, 1, -2, 1, 6, -18, 8, 89, -266, 62, 1684, -4710, -220, 35648, -91236, -34871, 803302, -1856874, -1448844, 18809694, -38816620, -48910700, 451491680, -820626294, -1522994404, 11015923292, -17319046712, -45512957516, 271664145264, -359911736252, -1327355044924
Offset: 0
-
a(n, s=2) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
A365115
G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^5.
Original entry on oeis.org
1, 1, 5, 20, 90, 440, 2236, 11720, 62960, 344690, 1916170, 10787762, 61380770, 352410760, 2039099640, 11878519460, 69608606348, 410056995475, 2426936098575, 14424334077975, 86055337016695, 515170271387970, 3093724519080210, 18631778892165080
Offset: 0
-
a(n, s=5) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
Showing 1-4 of 4 results.