|
|
FORMULA
| 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 = 2.
|
|
|
MAPLE
| restart; nmax:=15; mmax:=nmax: imax := nmax: i:=0: 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(j)*(x+1)^(j), j=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:=2; for n from m to nmax do a(n, m):= 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) od: seq(a(n, m), n=m..nmax);
|
