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Search: id:A035009
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| A035009 |
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STIRLING transform of [1,1,2,4,8,16,32, ...]. |
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+0
10
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| 1, 1, 3, 11, 47, 227, 1215, 7107, 44959, 305091, 2206399, 16913987, 136823263, 1163490499, 10366252031, 96491364675, 935976996127, 9440144423875, 98800604237119, 1071092025420867, 12008090971866207
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Numerators of sequence that shifts left one place under 1/2 order binomial transform. (Denominators are 2^(n-1) for n>0.) - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jul 31 2005
Row sums of triangle A137597 starting (1, 3, 11, 47, 227,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 29 2008
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FORMULA
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E.g.f.: [1 + exp(2exp(x)-2)]/2. - Emeric Deutsch, Feb 09, 2002
Recurrence : a(n+1) = 1 + 2*sum { j=1, n, binomial(n, j)*a(j) } - Jon Perry (perry(AT)globalnet.co.uk), Apr 25 2005
Define f_1(x),f_2(x),... such that f_1(x)=e^x and for n=2,3,... f_{n+1}(x)=diff(x*f_n(x),x). Then a(n)=e^{-2}*f_n(2). - Milan R. Janjic (agnus(AT)blic.net), May 30 2008
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MATHEMATICA
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1/(2*E^2)*Sum[(i + j)^n/(i!*j!), {i, 0, Infinity}, {j, 0, Infinity}] (* Starting from the 2nd term *) [From Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Dec 31 2008]
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CROSSREFS
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Equals (1/2) A001861(n), n>0.
Cf. A000110.
Cf. A137597.
Sequence in context: A118927 A062146 A090365 this_sequence A051296 A030832 A030865
Adjacent sequences: A035006 A035007 A035008 this_sequence A035010 A035011 A035012
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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