A135887 Column 2 of triangle Q = A135885; also equals column 0 of Q^3 = A135893.

1, 6, 42, 351, 3470, 39968, 528306, 7906598, 132426050, 2457643895, 50110693656, 1114365815786, 26856942480503, 697612318151050, 19435260247394150, 578255661792065917, 18303904706366202568, 614296560055922433760

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Example

Triangle Q = A135885 begins:
1;
2, 1;
6, 4, 1;
25, 20, 6, 1;
138, 126, 42, 8, 1;
970, 980, 351, 72, 10, 1;
8390, 9186, 3470, 748, 110, 12, 1; ...
where column k of Q equals column 0 of Q^(k+1) such that
column 0 of Q equals column 0 of P=A135880 shift left and Q=P^2.

Prog

(PARI) {a(n)=local(P=Mat(1), R, PShR); if(n==0, 1, for(i=0, n+1, PShR=matrix(#P, #P, r, c, if(r>=c, if(r==c, 1, if(c==1, 0, P[r-1, c-1])))); R=P*PShR; R=matrix(#P+1, #P+1, r, c, if(r>=c, if(r<#P+1, R[r, c], if(c==1, (P^2)[ #P, 1], (P^(2*c-1))[r-c+1, 1])))); P=matrix(#R, #R, r, c, if(r>=c, if(r<#R, P[r, c], (R^c)[r-c+1, 1])))); (P^2)[n+3, 3])}

Crossrefs

Cf. A135885 (Q), A135893 (Q^3), A135880; other columns: A135881, A135886.

Sequence in context: A300693 A222062 A074017 * A218817 A368321 A052589

Adjacent sequences: A135884 A135885 A135886 * A135888 A135889 A135890

Keyword

nonn

Author

Paul D. Hanna, Dec 15 2007

Status

approved