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Search: id:A112705
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| A112705 |
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Triangle built from partial sums of Catalan numbers A000108 multiplied by powers. |
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+0
12
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| 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 11, 4, 1, 1, 23, 51, 22, 5, 1, 1, 65, 275, 157, 37, 6, 1, 1, 197, 1619, 1291, 357, 56, 7, 1, 1, 626, 10067, 11497, 3941, 681, 79, 8, 1, 1, 2056, 64979, 107725, 46949, 9431, 1159, 106, 9, 1, 1, 6918, 431059, 1045948, 587621
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The column sequences (without leading zeros) begin with A000012 (powers of 1), A112705 (partial sums Catalan), A112696-A112704, for m=0..10.
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LINKS
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W. Lang: First 10 rows.
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FORMULA
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a(n, m)= sum(C(k)*m^k, k=0..n-m), n>m>0, with C(n):=A000108(n); a(n, n)=1; a(n, 0)=1; a(n, m)=0 if n<m.
G.f. for column m>=0 (without leading zeros): c(m*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
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CROSSREFS
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Row sums give A112706.
Sequence in context: A091150 A091351 A058730 this_sequence A070895 A127054 A125790
Adjacent sequences: A112702 A112703 A112704 this_sequence A112706 A112707 A112708
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 31 2005
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