A365114
G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^4.
Original entry on oeis.org
1, 1, 4, 14, 56, 241, 1080, 4998, 23704, 114588, 562552, 2797138, 14057140, 71288385, 364360204, 1874960408, 9706035408, 50510552881, 264096980192, 1386676113360, 7308650513232, 38654087828310, 205076534841112, 1091144400876394, 5820924498941668
Offset: 0
-
a(n, s=4) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
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));
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.