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Search: id:A073714
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| A073714 |
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Table T(n,m), read by antidiagonals, is generated by successive convolutions of this the first row sequence. Antidiagonals are read in the order (n,m) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),... |
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1
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 2, 1, 5, 10, 10, 7, 1, 1, 6, 15, 20, 18, 8, 1, 1, 7, 21, 35, 39, 27, 9, 3, 1, 8, 28, 56, 75, 68, 37, 14, 3, 1, 9, 36, 84, 132, 146, 108, 54, 20, 1, 1, 10, 45, 120, 217, 282, 260, 168, 81, 20, 6, 1, 11, 55, 165, 338, 504, 552, 440, 263, 106
(list; graph; listen)
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OFFSET
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0,5
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FORMULA
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Let first row sequence be a(n)=T(0, n); define f(x) = sum_{k=0..inf} a(k)x^k, then the n-th row is generated by: f(x)^(n+1) = sum_{k=0..inf} T(n, k)x^k.
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EXAMPLE
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Table read by antidiagonals gives first row; subsequent rows generated by convolutions of first row sequence.
1,_1,__1,___1,___2,___1,___1,___3,___3,___1,___1,___4,...
1,_2,__3,___4,___7,___8,___9,__14,__20,__20,__21,__32,...
1,_3,__6,__10,__18,__27,__37,__54,__81,_106,_132,_180,...
1,_4,_10,__20,__39,__68,__54,_168,_263,_388,_544,_768,...
1,_5,_15,__35,__75,_108,_260,_440,_730,1165,1781,2670,...
1,_6,_21,__56,_132,_282,_552,1014,1794,3058,5013,...
1,_7,_28,__84,_217,_504,1071,2122,4004,7252,...
1,_8,_36,_120,_338,_848,1940,4120,8271,...
1,_9,_45,_165,_504,1359,3327,7533,...
1,10,_55,_220,_725,2092,5455,...
1,11,_66,_286,1012,3113,...
1,12,_78,_364,1377,...
1,13,_91,_455,...
1,14,105,...
1,15,...
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CROSSREFS
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Sequence in context: A034253 A118687 A026022 this_sequence A144151 A022818 A050447
Adjacent sequences: A073711 A073712 A073713 this_sequence A073715 A073716 A073717
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 05 2002
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