A367236
G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^2)^2.
Original entry on oeis.org
1, 1, 2, 7, 26, 107, 462, 2074, 9572, 45147, 216638, 1054254, 5190710, 25810064, 129423512, 653740518, 3323270096, 16988894131, 87283137130, 450434292624, 2333851816654, 12136369892776, 63318984098996, 331347363084737, 1738713937163124, 9146850725274636
Offset: 0
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a(n, s=2, t=0, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A367237
G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 - x*A(x)^2)^2.
Original entry on oeis.org
1, 1, 4, 20, 114, 702, 4550, 30585, 211270, 1490561, 10695354, 77809481, 572608270, 4254996670, 31882486314, 240620654468, 1827464108766, 13956516915303, 107114560278680, 825727777034002, 6390721805005678, 49638977802126104, 386824024893533450
Offset: 0
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CoefficientList[Series[Root[-1 + #1 + x*#1^2 - 2*x*#1^3 - x^2*#1^4 + x^2*#1^5&, 1],{x,0,20}],x] (* Vaclav Kotesovec, Nov 13 2023 *)
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a(n, s=2, t=2, u=2) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
A367280
G.f. satisfies A(x) = 1 + x*A(x)^3 / (1 - x*A(x)^3)^2.
Original entry on oeis.org
1, 1, 5, 33, 251, 2073, 18069, 163600, 1523731, 14504988, 140499307, 1380322749, 13721269995, 137758098052, 1394840743638, 14227181658075, 146048314214619, 1507739540085350, 15643456882376418, 163036276218805231, 1706021256401103673
Offset: 0
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a(n, s=2, t=3, u=3) = sum(k=0, n, binomial(t*k+u*(n-k)+1, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+1));
Showing 1-3 of 3 results.