A088675 Eigenfunction of a sequence transformation.

0, 1, -2, 8, -36, 160, -656, 2368, -7664, 29440, -184896, 1174272, -3395200, -21222400, 178961920, 1638189056, -27449296640, -28875071488, 3234263731200, -10138343231488, -422012179953664, 3426627065331712, 59293997091528704

Offset

0,3

Comments

G.f. A(x) satisfies x=(1+4*A(x))A(A(x)).

Links

Table of n, a(n) for n=0..22.

Formula

a(n)=T(n,1), T(n,m)=1/2*(sum(k=1..n-m, 4^k*T(n-m,k)*binomial(k+m-1,m-1)*(-1)^(k))-sum(k=m+1..n-1, T(n,k)*T(k,m))), n>m, T(n,n)=1. [Vladimir Kruchinin, May 04 2012]

Prog

(PARI) a(n)=local(A); if(n<1, 0, A=x; for(k=1, n, A=Pol(A+serreverse(A+x*O(x^k))/(1+4*x))/2); polcoeff(A, n))
(Maxima) T(n, m):=if n=m then 1 else 1/2*(sum(4^k*T(n-m, k)*binomial(k+m-1, m-1)*(-1)^(k), k, 1, n-m)-sum(T(n, k)*T(k, m), k, m+1, n-1)); makelist(T(n, 1), n, 1, 10); [Vladimir Kruchinin, May 04 2012]

Crossrefs

Sequence in context: A123290 A321110 A228791 * A228197 A326244 A027743

Adjacent sequences: A088672 A088673 A088674 * A088676 A088677 A088678

Keyword

sign

Author

Michael Somos, Oct 04 2003

Status

approved