A096812 Forwards row convergent of triangle A096811, in which A096811(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and (k-2).

1, 1, 1, 2, 4, 8, 16, 34, 72, 156, 336, 746, 1652, 3696, 8330, 18816, 42904, 98166, 225148, 518386, 1199966, 2778270, 6472492, 15097226, 35311946, 82744656, 194406728, 457526278, 1078889548, 2549790238, 6034719500, 14305107700, 33965903292, 80747360636, 192219095518, 458252713872, 1093494859572, 2613290156486, 6251109118574, 14970041423150

Offset

0,4

Comments

Backwards row convergent of A096811 is A096813.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..50

Formula

a(0)=a(1)=1; for n>1, a(n) = Sum_{k=0..n-2} A096811(n-2, n-k-2)*a(k+1).

Prog

(PARI) {A096811(n, k)=if(n<k || k<0, 0, if(k<=1 || k==n, 1, sum(j=1, k-1, A096811(n-k, j)*A096811(k-2, k-j-1))))} \ {a(n)=if(n<0, 0, if(n<=1, 1, sum(k=0, n-2, T(n-2, n-k-2)*a(k+1))))}

Crossrefs

Cf. A096811, A096813.

Sequence in context: A288260 A006210 A288176 * A006981 A003427 A333647

Adjacent sequences: A096809 A096810 A096811 * A096813 A096814 A096815

Keyword

nonn

Author

Paul D. Hanna, Jul 20 2004

Status

approved