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Search: id:A086672
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| A086672 |
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Stirling transform of Catalan numbers: Sum_{k=0..n} Stirling1(n,k)*binomial(2*k,k)/(k+1). |
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+0
2
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| 1, 1, 1, 1, 0, 1, -5, 29, -196, 1518, -13266, 129163, -1386572, 16270671, -207195495, 2845705719, -41930575740, 659781404944, -11041824881696, 195839234324062, -3669384701403344
(list; graph; listen)
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OFFSET
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0,7
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FORMULA
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E.g.f.: hypergeom([1/2], [2], 4*ln(1+x)) = (1+x)^2*(BesselI(0, 2*ln(1+x))-BesselI(1, 2*ln(1+x))).
Let C(m) be the m-th Catalan number, A000108(m). Let S(m, n) = an unsigned Stirling number of the first kind. Then a(m) = sum{k=0 to m} S(m, k) C(k) (-1)^(k+m). - Leroy Quet, Jan 23, 2004.
E.g.f. f(x) satisfies f(x) = 1 + integral{0 to x} f(y) f((x-y)/(1+y))/(1+y) dy. - Leroy Quet(qq-quet(AT)mindspring.com), Jan 25 2004
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CROSSREFS
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Cf. A000108, A008275, A064856.
Sequence in context: A142980 A062191 A095000 this_sequence A094710 A108453 A004213
Adjacent sequences: A086669 A086670 A086671 this_sequence A086673 A086674 A086675
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KEYWORD
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easy,sign
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Sep 12 2003
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