2,2

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.

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);

Second left hand column of the EG1 triangle A162005.

Other left hand columns are A000182 and A162007.

Related to A094665, A083061 and A156919.

A000079 and A036289 appear in the Maple program.

Sequence in context: A097579 A091549 A034904 this_sequence A025753 A160312 A132503

Adjacent sequences: A162003 A162004 A162005 this_sequence A162007 A162008 A162009

easy,nonn

Johannes W. Meijer (meijgia(AT)hotmail.com), Jun 27 2009