A144061 - OEIS

%I #3 Mar 03 2013 12:57:23

%S 1,1,1,1,3,2,1,5,10,6,1,7,22,42,22,1,9,38,114,198,94,1,11,58,234,638,

%T 1034,454,1,13,82,414,1518,3854,5902,2430,1,15,110,666,3058,10434,

%U 24970,36450,14214,1,17,142,1002,5522,23594,75818,172530,241638,89918

%N Eigentriangle generated from A109128, row sums = expansion of {2(exp(x)-1)}

%C Row sums = A001861: (1, 2, 6, 22, 94, 454, 2430,...) = expansion of {2(exp(x)-1)}

%C Right border = A001861 shifted: (1, 1, 2, 6, 22, 94,...).

%C Sum of n-th row terms = rightmost term of next row.

%F T(n,k) = A109128(n,k)*A001861(k-1).

%F A109128 = (2*binomial(n,k) - 1): (1; 1,1; 1,3,1; 1,5,5,1;...).

%F A001861(k-1) = A001861 shifted one place, = (1, 1, 2, 6, 22, 94, 454,...).

%e First few rows of the triangle =

%e 1;

%e 1, 1;

%e 1, 3, 2;

%e 1, 5, 10, 6;

%e 1, 7, 22, 42, 22;

%e 1, 9, 38, 114, 198, 94;

%e 1, 11, 58, 234, 638, 1034, 454;

%e 1, 13, 82, 414, 1518, 3854, 5902, 2430;

%e 1, 15, 110, 666, 3058, 10434, 24970, 36450, 14214;

%e ...

%e Example: row 3 = (1, 5, 10, 6) = termwise products of (1, 5, 5, 1) and (1, 1, 2, 6), where (1, 5, 5, 1) = row 3 of triangle A109128 and (1, 1, 2, 6) = the first 4 terms of A001861 shifted.

%Y A109128, Cf. A001861

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_ & _Roger L. Bagula_, Sep 09 2008