A366694
G.f. satisfies A(x) = (1 + x)^2 + x*A(x)^2.
Original entry on oeis.org
1, 3, 7, 23, 88, 363, 1576, 7091, 32768, 154588, 741442, 3604495, 17721394, 87960004, 440165522, 2218289051, 11248850578, 57354875692, 293860786178, 1512169500356, 7811933144432, 40499933496818, 210643657689644, 1098802033533295, 5747266778089846
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*(k+1), n-k)*binomial(2*k, k)/(k+1));
A381939
G.f. A(x) satisfies A(x) = (1 + x)^3 * B(x*A(x)), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 4, 13, 74, 568, 4872, 44576, 425936, 4199616, 42404096, 436238592, 4556085248, 48179319808, 514825553408, 5550284218368, 60296483084288, 659417378381824, 7253858445852672, 80209754567786496, 891027699137609728, 9939286070426992640, 111286739309529858048
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*k+1, k)*binomial(3*k+3, n-k)/(4*k+1));
A381942
G.f. A(x) satisfies A(x) = (1 + x)^3 * B(x*A(x)), where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 4, 14, 96, 905, 9550, 107552, 1265372, 15364920, 191090255, 2421646300, 31157939594, 405932855044, 5344301858465, 70990458721140, 950263442420120, 12805328720666376, 173574888045493536, 2365049262321662145, 32374714068988416170, 445017678283209218750, 6140131349497715896244
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(3*k+3, n-k)/(5*k+1));
Showing 1-3 of 3 results.