A379283
G.f. A(x) satisfies A(x) = 1/( (1 - x*A(x)^3) * (1 - x*A(x)) )^2.
Original entry on oeis.org
1, 4, 42, 612, 10387, 192312, 3766316, 76716624, 1608691229, 34495221722, 752911467734, 16671973428486, 373609441084507, 8457057155407906, 193087102810266948, 4441320670474030222, 102821800799622552713, 2394063264658388861914, 56025225620739219372819
Offset: 0
-
a(n) = 2*sum(k=0, n, binomial(2*n+5*k+2, k)*binomial(3*n+3*k+1, n-k)/(2*n+5*k+2));
A379328
G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x)^3) * (1 + 2*x*A(x)) ).
Original entry on oeis.org
1, 2, 8, 44, 272, 1808, 12616, 91136, 675712, 5112576, 39316480, 306402304, 2414543328, 19207303168, 154030314752, 1243912552448, 10107398806016, 82573989969920, 677862373390592, 5588755066388480, 46257005500080128, 384210240316375040, 3201482490107076608
Offset: 0
-
a(n) = 2^n*sum(k=0, n, binomial(n/2+k+1/2, k)*binomial(n/2+k+1/2, n-k)/(n+2*k+1));
A379279
G.f. A(x) satisfies A(x) = ( (1 + x*A(x)^2) * (1 + x*A(x)) )^2.
Original entry on oeis.org
1, 4, 30, 288, 3125, 36490, 447478, 5683186, 74105002, 986302778, 13344661479, 182998935930, 2537838036761, 35530970858236, 501523116910044, 7129275916213606, 101973703002773268, 1466574750062589956, 21194869324964207133, 307642575576365729486, 4482940969372057898247
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*n+2*k+2, k)*binomial(2*n+2*k+2, n-k)/(n+k+1));
Showing 1-3 of 3 results.