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Search: id:A090753
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| A090753 |
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Coefficients of power series A(x) such that n-th term of A(x)^n = n!*n*x^(n-1), for n>0. |
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3
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| 1, 2, 2, 4, 16, 88, 600, 4800, 43680, 443296, 4949920, 60217408, 792134528, 11200176128, 169375195136, 2728019576832, 46626359376384, 842947307334144, 16073131554826752, 322403473258650624, 6786861273524305920
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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At n=4 the 4-th term of A(x)^4 is 4!*4x^3 = 96*x^3, as demonstrated by A(x)^4 = 1 + 8*x + 32*x^2 + 96*x^3 + 296*x^4 + ... See also A075834.
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FORMULA
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a(0)=1, a(1)=2; a(n)= sum_{j=2..(n-2)} (j-1)*a(j)*a(n-j), n>=2 . Sum_{j>=0} a(j)*A090238(n-1, k+j-1) = A090238(n, k).
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(x/serreverse(sum(k=1, n+1, k!*x^k, x^2*O(x^n))), n)) - Michael Somos Feb 14 2004
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CROSSREFS
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Sequence in context: A102864 A009542 A032318 this_sequence A091788 A063401 A129614
Adjacent sequences: A090750 A090751 A090752 this_sequence A090754 A090755 A090756
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KEYWORD
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nonn
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 06 2004
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