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A138415
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Binomial transform of A000957.
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3
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0, 1, 2, 4, 10, 31, 110, 421, 1686, 6961, 29392, 126292, 550360, 2426503, 10803802, 48507844, 219377950, 998436793, 4569488372, 21016589074, 97090411020, 450314942683, 2096122733212, 9788916220519, 45850711498860, 215348942668681, 1013979873542690, 4785437476592806
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OFFSET
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0,3
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LINKS
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FORMULA
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Recurrence: 2*n*a(n) = 3*(5*n - 6)*a(n-1) - (29*n - 57)*a(n-2) + 3*(7*n - 18)*a(n-3) - 5*(n-3)*a(n-4).
a(n) ~ 5^(n + 3/2) / (72 * sqrt(Pi) * n^(3/2)). (End)
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MATHEMATICA
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Table[Sum[Binomial[n, k]*(2^k * (2*k-1)!! * Hypergeometric2F1Regularized[2, 2*k+1, k+2, -1] - 3*(-1)^k/2^(k+1)), {k, 1, n}], {n, 0, 30}] (* Vaclav Kotesovec, Oct 30 2017 *)
RecurrenceTable[{a[0]==0, a[1]==1, a[2]==2, a[3]==4, a[n]==(3(5n-6)a[n-1]-(29n-57) a[n-2]+3(7n-18)a[n-3]-5(n-3)a[n-4])/(2n)}, a, {n, 30}] (* Harvey P. Dale, Nov 22 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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