A108994 Third diagonal of triangle A108990, in which the g.f. of row n, R_n(x), satisfies: [x^k] R_{n+1}(x) = [x^k] (1 + x*R_n(x))^(n+1) for k=0..n+1.

1, 3, 18, 180, 2670, 54096, 1411228, 45421776, 1747674405, 78485504845, 4037946005808, 234494393383614, 15187062546935643, 1086079262127563445, 85049134680670591560, 7241328591814507465712, 666283956766298002183275

Offset

0,2

Comments

a(n) is divisible by (n+1)*(n+2)/2.

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = A108990(n+2, n) for n>=0. a(n) = (n+2)/2*A108995(n) for n>=0.

Prog

(PARI) {a(n)=local(F=1+x*O(x^n)); for(m=1, n+2, F=(1+x*F)^m); polcoeff(F, n)}

Crossrefs

Cf. A108990, A108991, A108992, A108993, A108995, A108996.

Sequence in context: A223895 A111465 A247029 * A006472 A132853 A259666

Adjacent sequences: A108991 A108992 A108993 * A108995 A108996 A108997

Keyword

nonn

Author

Paul D. Hanna, Jun 15 2005

Status

approved