A121424 Rectangular table, read by antidiagonals, where row n is equal to column 0 of matrix power A121412^(n+1) for n>=0.
1, 1, 1, 1, 2, 3, 1, 3, 7, 18, 1, 4, 12, 43, 170, 1, 5, 18, 76, 403, 2220, 1, 6, 25, 118, 711, 5188, 37149, 1, 7, 33, 170, 1107, 9054, 85569, 758814, 1, 8, 42, 233, 1605, 13986, 147471, 1725291, 18301950, 1, 9, 52, 308, 2220, 20171, 225363, 2938176, 41145705
Offset: 0
Examples
Table of column 0 in matrix powers of triangle H=A121412 begins: H^1: 1, 1, 3, 18, 170, 2220, 37149, 758814, 18301950,... H^2: 1, 2, 7, 43, 403, 5188, 85569, 1725291, 41145705,... H^3: 1, 3, 12, 76, 711, 9054, 147471, 2938176, 69328365,... H^4: 1, 4, 18, 118, 1107, 13986, 225363, 4441557, 103755660,... H^5: 1, 5, 25, 170, 1605, 20171, 322075, 6285390, 145453290,... H^6: 1, 6, 33, 233, 2220, 27816, 440785, 8526057, 195579123,... H^7: 1, 7, 42, 308, 2968, 37149, 585046, 11226958, 255436293,... H^8: 1, 8, 52, 396, 3866, 48420, 758814, 14459138, 326487241,... H^9: 1, 9, 63, 498, 4932, 61902, 966477, 18301950, 410368743,... Rearrangement of the upper half of the table forms A121430, which is the number of subpartitions of partition [0,1,1,2,2,2,3,3,3,3,4,...]: 1, 1,2, 3,7,12, 18,43,76,118, 170,403,711,1107,1605, 2220,...
Crossrefs
Programs
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PARI
{T(n,k)=local(H=Mat(1), B); for(m=1, k+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=1, B[i, j]=(H^i)[i-1, j]); )); H=B); return((H^(n+1))[k+1, 1])}