A125277 Eigensequence of triangle A110616: a(n) = Sum_{k=0..n-1} A110616(n-1,k)*a(k) for n>0 with a(0)=1.

1, 1, 2, 7, 32, 169, 981, 6113, 40386, 280871, 2047316, 15595317, 123876270, 1024188790, 8799533250, 78443220865, 724472766347, 6922133112818, 68331103658847, 695983854400857, 7305630631254242, 78941171881894716

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = Sum_{k=0..n-1} a(k) * C(3*n-2*k-2,n-k-1)*(k+1)/(3*n-2*k-2) for n>0 with a(0)=1.

Example

a(3) = 3*(1) + 2*(1) + 1*(2) = 7;
a(4) = 12*(1) + 7*(1) + 3*(2) + 1*(7) = 32;
a(5) = 55*(1) + 30*(1) + 12*(2) + 4*(7) + 1*(32) = 169.
Triangle A110616(n,k) = C(3*n-2*k+1, n-k)*(k+1)/(3*n-2*k+1) begins:
1;
1, 1;
3, 2, 1;
12, 7, 3, 1;
55, 30, 12, 4, 1;
273, 143, 55, 18, 5, 1;
1428, 728, 273, 88, 25, 6, 1; ...
where g.f. of column k = G001764(x)^(k+1)
and G001764(x) = 1 + x*G001764(x)^3 is the g.f. of A001764.

Prog

(PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, a(k)*binomial(3*n-2*k-2, n-k-1)*(k+1)/(3*n-2*k-2)))}

Crossrefs

Cf. A110616, A001764, A091768.

Sequence in context: A330075 A115197 A107593 * A321688 A222013 A179488

Adjacent sequences: A125274 A125275 A125276 * A125278 A125279 A125280

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2006

Status

approved