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A162007
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Third left hand column of the EG1 triangle A162005
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7
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1, 270, 36096, 4766048, 704357760, 120536980224, 24060789342208, 5590122715250688, 1503080384197754880, 464520829174515630080, 163839204411117787938816, 65500849343294249018327040
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OFFSET
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3,2
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LINKS
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FORMULA
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a(n) = sum((-1)^(m-p-1)*sum(2^(n-q-1)*binomial(n-q-1,m-p-1)*A094665(n-1,q)* A156919(q,p),q=1..n-m+p), p=0..m-1) with m = 3.
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MAPLE
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nmax := 14; mmax := nmax: imax := nmax: T1(0, x) := 1: T1(0, x+1) := 1: for i from 1 to imax do T1(i, x) := expand((2*x+1)*(x+1)*T1(i-1, x+1) - 2*x^2*T1(i-1, x)): dx := degree(T1(i, x)): for k from 0 to dx do c(k) := coeff(T1(i, x), x, k) od: T1(i, x+1) := sum(c(j1)*(x+1)^(j1), j1 = 0..dx): od: for i from 0 to imax do for j from 0 to i do A083061(i, j) := coeff(T1(i, x), x, j) od: od: for n from 0 to nmax do for k from 0 to n do A094665(n+1, k+1) := A083061(n, k) od: od: A094665(0, 0) := 1: for n from 1 to nmax do A094665(n, 0) := 0 od: for m from 1 to mmax do A156919(0, m) := 0 end do: for n from 0 to nmax do A156919(n, 0) := 2^n end do: for n from 1 to nmax do for m from 1 to mmax do A156919(n, m) := (2*m+2)*A156919(n-1, m) + (2*n-2*m+1) * A156919(n-1, m-1) end do end do: m:=3; for n from m to nmax do a(n, m) := sum((-1)^(m-p1-1)*sum(2^(n-q-1)*binomial(n-q-1, m-p1-1) * A094665(n-1, q) * A156919(q, p1), q=1..n-m+p1), p1=0..m-1) od: seq(a(n, m), n = m..nmax);
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CROSSREFS
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Third left hand column of the EG1 triangle A162005.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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