A365113
G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^3.
Original entry on oeis.org
1, 1, 3, 9, 31, 114, 438, 1739, 7077, 29364, 123756, 528324, 2279868, 9928679, 43580301, 192601419, 856317717, 3827501985, 17188943523, 77521747638, 350959738842, 1594390493067, 7266093316649, 33209221327752, 152182572790008, 699083290518817, 3218624408121555
Offset: 0
-
a(n, s=3) = sum(k=0, n, 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));
A365112
G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^5.
Original entry on oeis.org
1, 1, -5, 10, 20, -220, 624, 940, -15220, 52090, 49310, -1254070, 4951430, 2039640, -113088840, 505430700, -42379684, -10748423405, 53899438385, -29300595085, -1054751754795, 5914944193114, -5760460624890, -105478270711140, 661900612108440, -914408777470140
Offset: 0
-
a(n, s=5) = 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));
Showing 1-4 of 4 results.