A370472
G.f. satisfies A(x) = 1 + x * A(x) * (1 - A(x) + A(x)^2 - A(x)^3 + A(x)^4).
Original entry on oeis.org
1, 1, 3, 15, 88, 565, 3844, 27228, 198670, 1482981, 11271117, 86926262, 678568982, 5351340410, 42570335161, 341201704970, 2752693408051, 22335989938093, 182166978172055, 1492496248447713, 12278191839580716, 101382009468089580, 839932374157895727
Offset: 0
-
a(n) = sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+1/2, n)/(n+5*k+1));
A370475
G.f. satisfies A(x) = 1 + x * A(x)^(3/2) * (1 + A(x)^(5/2)).
Original entry on oeis.org
1, 2, 11, 86, 785, 7818, 82360, 902394, 10178528, 117402240, 1378372807, 16417823232, 197903156219, 2409689022268, 29593911665705, 366158474520010, 4559848894822462, 57109656154370922, 718896822713092457, 9090475112572839810, 115417175337050727590
Offset: 0
-
a(n) = sum(k=0, n, binomial(n, k)*binomial(3*n/2+5*k/2+1, n)/(3*n/2+5*k/2+1));
A371723
G.f. satisfies A(x) = ( 1 + x * A(x)^(1/4) * (1 + A(x)^(5/4)) )^2.
Original entry on oeis.org
1, 4, 18, 100, 623, 4156, 29032, 209656, 1552535, 11724904, 89958000, 699213444, 5494103979, 43570067100, 348274269966, 2803139823512, 22698137859554, 184779492011244, 1511406790180350, 12415340284461312, 102377122022648745, 847144310799588732
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+2, n)/(n/2+5*k/2+2));
A371725
G.f. satisfies A(x) = ( 1 + x * A(x)^(1/5) * (1 + A(x)) )^(5/2).
Original entry on oeis.org
1, 5, 25, 145, 925, 6266, 44245, 322075, 2399725, 18211775, 140285018, 1093997085, 8620125925, 68523526635, 548867710575, 4425604018075, 35892727867805, 292604563615625, 2396375011877275, 19707111724556025, 162671328783723678, 1347313142469049275
Offset: 0
-
a(n) = sum(k=0, n, binomial(n, k)*binomial(n/2+5*k/2+5/2, n)/(n/5+k+1));
Showing 1-4 of 4 results.