A375393
a(0) = 1; a(n) = Sum_{k=0..n-1} (4*k+3) * a(k) * a(n-k-1).
Original entry on oeis.org
1, 3, 30, 483, 10314, 268686, 8167068, 281975715, 10863651474, 461227101210, 21377716429860, 1073816307452430, 58106804389870500, 3370330005649001532, 208635817503306332088, 13731856676157543219747, 957698874584753026878306, 70562301536089812703526370, 5477354759932929856218644820
Offset: 0
-
a[0] = 1; a[n_] := a[n] = Sum[(4 k + 3) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[] = 0; Do[A[x] = 1 + 3 x A[x]^2 + 4 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
A376086
a(0) = 1; a(n) = Sum_{k=0..n-1} (3*k+2) * a(k) * a(n-k-1).
Original entry on oeis.org
1, 2, 14, 160, 2444, 45792, 1005480, 25169760, 705321200, 21841420384, 740194188032, 27243674154368, 1082259310732096, 46159435144505600, 2104195645965319680, 102113572703197079040, 5256795948307255075584, 286171738279517073904128, 16427146596936396844976640
Offset: 0
-
a[0] = 1; a[n_] := a[n] = Sum[(3 k + 2) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[] = 0; Do[A[x] = 1 + 2 x A[x]^2 + 3 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
A376087
a(0) = 1; a(n) = Sum_{k=0..n-1} (4*k+1) * a(k) * a(n-k-1).
Original entry on oeis.org
1, 1, 6, 65, 994, 19386, 456940, 12594465, 396969930, 14078044862, 554782989908, 24053551260186, 1138039204281236, 58353983394380500, 3223791843357228120, 190914111715994215905, 12065701995815379444954, 810602692757305194731094, 57688894099612173692496580
Offset: 0
-
a[0] = 1; a[n_] := a[n] = Sum[(4 k + 1) a[k] a[n - k - 1], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; A[] = 0; Do[A[x] = 1 + x A[x]^2 + 4 x^2 A'[x] A[x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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