A381911
Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 2, 9, 55, 394, 3102, 25969, 226891, 2045342, 18883205, 177640462, 1696658418, 16408796013, 160366113609, 1581329919636, 15713344659359, 157187582466527, 1581676730708500, 15998326150898211, 162571286470135097, 1658893916098102321, 16991130941208846890
Offset: 0
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Table[Sum[Binomial[n + 3*k + 1, k] * Binomial[2*n - k, n - k]/(n + 3*k + 1), {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Mar 22 2025 *)
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n-k, n-k)/(n+3*k+1));
A381913
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 4, 28, 245, 2422, 25860, 291106, 3405405, 41014131, 505344113, 6341182427, 80768735045, 1041645452650, 13575670575944, 178528253213469, 2366073408348545, 31571528771106126, 423794981085407622, 5718929869862880055, 77539914280883389432, 1055790501909183080512
Offset: 0
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(4*n-k+2, n-k)/(n+3*k+1));
A381915
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 3, 18, 145, 1378, 14515, 163700, 1936414, 23716654, 298216851, 3827542585, 49938733635, 660366743580, 8830549084588, 119205253249287, 1622258295003714, 22232669093660250, 306569446979862205, 4250285556933578693, 59210418891925845529, 828417259759216617257
Offset: 0
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a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(3*n-k+1, n-k)/(n+4*k+1));
Showing 1-3 of 3 results.