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
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(4*n-k+2, n-k)/(n+3*k+1));
A381914
Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 2, 10, 72, 624, 6009, 61809, 664813, 7384613, 84045565, 974913510, 11483316680, 136974177209, 1651166320547, 20083352214058, 246168280262403, 3037682020219285, 37706043912831337, 470482875049515074, 5897864081341146065, 74243055437832292562, 938101296155866961124
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(2*n-k, n-k)/(n+4*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));
A381947
G.f. A(x) satisfies A(x) = B(x*A(x)) / (1 - x)^3, where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 4, 17, 111, 1001, 10507, 118986, 1411789, 17307078, 217422098, 2784080234, 36201950786, 476725871599, 6344524132503, 85198695369123, 1152990558752089, 15708685673520617, 215287198676732925, 2965962577091646604, 41052101428818066604, 570583013508324005560
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(n+2*k+2, n-k)/(5*k+1));
Showing 1-4 of 4 results.