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Search: id:A048786
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| A048786 |
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Triangle of coefficients of certain exponential convolution polynomials. |
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+0
5
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| 1, 8, 1, 96, 24, 1, 1536, 576, 48, 1, 30720, 15360, 1920, 80, 1, 737280, 460800, 76800, 4800, 120, 1, 20643840, 15482880, 3225600, 268800, 10080, 168, 1, 660602880, 578027520, 144506880, 150552800, 752640, 18816, 224, 1
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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i) p(n,x) := sum(a(n,m)*x^m,m=1..n), p(0,x) := 1, are monic polynomials satisfying p(n,x+y)= sum(binomial(n,k)*p(k,x)*p(n-k,y),k=0..n), (exponential convolution polynomials). ii) In the terminology of the umbral calculus (see reference) p(n,x) are called associated to f(t)= t/(1+4*t). iii) a(n,1)= A034177(n).
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REFERENCES
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S. Roman, The Umbral Calculus, Academic Press, New York, 1984
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FORMULA
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a(n, m) = n!*4^(n-m)*binomial(n-1, m-1)/m!, n >= m >= 1; a(n, m) := 0, m>n; a(n, m) = (n!/m!)*A038231(n-1, m-1) = 4^(n-m)*A008297(n, m) (Lah-triangle).
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CROSSREFS
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Cf. A034177, A038231, A008297.
Sequence in context: A051379 A143499 A114152 this_sequence A132056 A051187 A021850
Adjacent sequences: A048783 A048784 A048785 this_sequence A048787 A048788 A048789
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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