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A078938
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Cube of lower triangular matrix of A056857 (successive equalities in set partitions of n).
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16
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1, 3, 1, 12, 6, 1, 57, 36, 9, 1, 309, 228, 72, 12, 1, 1866, 1545, 570, 120, 15, 1, 12351, 11196, 4635, 1140, 180, 18, 1, 88563, 86457, 39186, 10815, 1995, 252, 21, 1, 681870, 708504, 345828, 104496, 21630, 3192, 336, 24, 1, 5597643, 6136830, 3188268
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OFFSET
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0,2
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COMMENTS
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Riordan array [exp(3*exp(x)-3),x], whose production matrix has e.g.f. exp(x*t)(t+3*exp(x)). [From Paul Barry, Nov 26 2008]
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LINKS
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FORMULA
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PE=exp(matpascal(5))/exp(1); A = PE^3; a(n)= A[ n,sequentially read ] with exact integer arithmetic: PE=exp(matpascal(5)-matid(6)); A = PE^3; a(n)=A[ n,sequentially read] - Gottfried Helms, Apr 08 2007
Exponential function of 3*Pascal's triangle (taken as a lower triangular matrix) divided by e^3: [A078938] = (1/e^3)*exp(3*[A007318]) = [A056857]^3.
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EXAMPLE
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Rows:
1,
3,1,
12,6,1,
57,36,9,1,
309,228,72,12,1,
1866,1545,570,120,15,1,
12351,11196,4635,1140,180,18,1,
...
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PROG
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(PARI) m=matpascal(5)-matid(6); pe=matid(6)+m/1! + m^2/2!+m^3/3!+m^4/4!+m^5/5! ; A = pe^3 - Gottfried Helms, Apr 08 2007
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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