A096813 Backwards 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).

0, 1, 1, 2, 4, 8, 18, 40, 92, 210, 490, 1178, 2834, 6908, 16996, 41874, 103632, 260512, 654600, 1653944, 4199426, 10727056, 27403928, 70312316, 181295568, 468321714, 1212382254, 3147806654, 8192069326, 21373640244, 55866022580, 146245331310, 383916472318, 1009104851284, 2656963351444, 7004641163440, 18494746329858, 48903314780234, 129515618740984, 343289075820158, 911136373946940

Offset

0,4

Comments

This is the convergent of the rows of triangle A096811 when the rows are read from right to left; includes an initial zero to comply with the definition. The forwards row convergent of A096811 is A096812.

Links

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

Formula

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

Crossrefs

Cf. A096811, A096813.

Sequence in context: A367659 A000967 A288309 * A058387 A330052 A317787

Adjacent sequences: A096810 A096811 A096812 * A096814 A096815 A096816

Keyword

nonn

Author

Paul D. Hanna, Jul 20 2004

Status

approved