A088675 G.f. A(x) satisfies x = (1 + 4*A(x)) * A(A(x)).

1, -2, 8, -36, 160, -656, 2368, -7664, 29440, -184896, 1174272, -3395200, -21222400, 178961920, 1638189056, -27449296640, -28875071488, 3234263731200, -10138343231488, -422012179953664, 3426627065331712, 59293997091528704, -908697763346808832, -8627147856050937856

Offset

1,2

Comments

Eigenfunction of a sequence transformation.

Links

Paul D. Hanna, Table of n, a(n) for n = 1..400

Formula

a(n) = T(n,1), where 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

G.f. A(x) satisfies x = A( (1 + 4*x) * A(x) ). - Paul D. Hanna, Jan 13 2026

Example

G.f.: A(x) = x - 2*x^2 + 8*x^3 - 36*x^4 + 160*x^5 - 656*x^6 + 2368*x^7 - 7664*x^8 + 29440*x^9 - 184896*x^10 + ...

Prog

(PARI) {a(n) = my(A); if(n<1, 0, A=x; for(k=1, n, A = Pol(A + serreverse(A + x*O(x^k))/(1+4*x))/2); polcoef(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, 0, 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

Extensions

Changed name to the formula that was given in comments. - Paul D. Hanna, Jan 13 2026

Status

approved