A346680
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(4*k,k) / (3*k + 1).
Original entry on oeis.org
1, 0, 4, 18, 122, 847, 6237, 47583, 373149, 2989111, 24354777, 201214021, 1681719343, 14193619647, 120800146953, 1035593096367, 8934344395053, 77510878324671, 675799844685937, 5918354494345863, 52037647837001257, 459200394617540288, 4065477723321641932
Offset: 0
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Table[Sum[(-1)^(n - k) Binomial[4 k, k]/(3 k + 1), {k, 0, n}], {n, 0, 22}]
nmax = 22; A[] = 0; Do[A[x] = 1/(1 + x) + x (1 + x)^3 A[x]^4 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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a(n) = sum(k=0, n, (-1)^(n-k)*binomial(4*k, k)/(3*k + 1)); \\ Michel Marcus, Jul 29 2021
A346681
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(5*k,k) / (4*k + 1).
Original entry on oeis.org
1, 0, 5, 30, 255, 2275, 21476, 210404, 2120041, 21830314, 228713056, 2430255074, 26128088701, 283703487059, 3106713300821, 34270543858459, 380471319687826, 4247891403168599, 47665096853113576, 537244509843680309, 6079834137116933061, 69054467456964456599
Offset: 0
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Table[Sum[(-1)^(n - k) Binomial[5 k, k]/(4 k + 1), {k, 0, n}], {n, 0, 21}]
nmax = 21; A[] = 0; Do[A[x] = 1/(1 + x) + x (1 + x)^4 A[x]^5 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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a(n) = sum(k=0, n, (-1)^(n-k)*binomial(5*k, k)/(4*k + 1)); \\ Michel Marcus, Jul 29 2021
A346682
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(6*k,k) / (5*k + 1).
Original entry on oeis.org
1, 0, 6, 45, 461, 5020, 57812, 691586, 8512048, 107095262, 1371219004, 17808830924, 234048288772, 3106795261083, 41593689788637, 560980967638479, 7614970691479315, 103957059568762775, 1426355910771621805, 19658792867492660060, 272046427837226505466
Offset: 0
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Table[Sum[(-1)^(n - k) Binomial[6 k, k]/(5 k + 1), {k, 0, n}], {n, 0, 20}]
nmax = 20; A[] = 0; Do[A[x] = 1/(1 + x) + x (1 + x)^5 A[x]^6 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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a(n) = sum(k=0, n, (-1)^(n-k)*binomial(6*k, k)/(5*k + 1)); \\ Michel Marcus, Jul 29 2021
A346683
a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(7*k,k) / (6*k + 1).
Original entry on oeis.org
1, 0, 7, 63, 756, 9716, 132062, 1865626, 27124049, 403197584, 6100155272, 93626517858, 1454221328232, 22815183746508, 361030984965596, 5755543515895284, 92350704790963431, 1490287557170676816, 24171116970619575559, 393808998160695560841, 6442255541764422795759
Offset: 0
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Table[Sum[(-1)^(n - k) Binomial[7 k, k]/(6 k + 1), {k, 0, n}], {n, 0, 20}]
nmax = 20; A[] = 0; Do[A[x] = 1/(1 + x) + x (1 + x)^6 A[x]^7 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
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a(n) = sum(k=0, n, (-1)^(n-k)*binomial(7*k, k)/(6*k + 1)); \\ Michel Marcus, Jul 29 2021
Showing 1-4 of 4 results.