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A111537
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Column 1 of triangle A111536.
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5
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1, 2, 8, 44, 296, 2312, 20384, 199376, 2138336, 24936416, 314142848, 4252773824, 61594847360, 950757812864, 15586971531776, 270569513970944, 4959071121374720, 95721139472072192, 1941212789888952320
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums of triangle in A200659. From DELEHAM Philippe, Nov 21 2011.
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FORMULA
| a(n) = A111536(n+1, 1) = 2*A111536(n, 0) = 2*A111529(n) for n>=1. G.f.: Log(Sum_{n>=0} (n+1)!*x^n) = Sum_{n>=1} a(n)*x^n/n.
a(n+1)=(n+3)!-2*(n+2)!-sum((n-k+1)!*a(k+1),k=0..n-1)
a(n+1) is the moment of order n for the measure of density x*exp(-x)/((x*exp(-x)*Ei(x)-1)^2+(Pi*x*exp(-x))^2) on the interval 0..infinity
G.f.: 1/(1-2x/(1-2x/(1-3x/(1-3x/(1-4x/(1-4x/(1-5x/(1-...(continued fraction).- From DELEHAM Philippe, Nov 21 2011.
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PROG
| (PARI) {a(n)=if(n<0, 0, (matrix(n+2, n+2, m, j, if(m==j, 1, if(m==j+1, -m+1, -(m-j-1)*polcoeff(log(sum(i=0, m, (i+1)!/1!*x^i)), m-j-1))))^-1)[n+2, 2])}
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CROSSREFS
| Cf. A111536, A111529, A200659.
Sequence in context: A201374 A120928 A179489 * A051045 A112912 A124467
Adjacent sequences: A111534 A111535 A111536 * A111538 A111539 A111540
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 06 2005
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