Search: id:A000457
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%I A000457 M4736 N2028
%S A000457 1,10,105,1260,17325,270270,4729725,91891800,1964187225,45831035250,
%T A000457 1159525191825,31623414322500,924984868933125,28887988983603750,
%U A000457 959493919812553125,33774185977401870000,1255977541034632040625
%N A000457 Exponential generating function: (1+3x)/(1-2x)^(7/2).
%D A000457 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000457 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000457 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 256.
%D A000457 F. N. David and D. E. Barton, Combinatorial Chance. Hafner, NY, 1962, 
               p. 296.
%D A000457 C. Jordan, On Stirling's Numbers, Tohoku Math. J., 37 (1933), 254-278.
%D A000457 C. Jordan, Calculus of Finite Differences. Budapest, 1939, p. 152.
%H A000457 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StirlingNumberoftheFirstKind.html">Link to a section of The World 
               of Mathematics.</a>
%F A000457 (2n+3)!/ [3!*n!*2^n ].
%F A000457 a(n)=(n+1)*(2*n+3)!!/3, n>=0, with (2*n+3)!! = A001147(n+2).
%Y A000457 Equals (1/2)*A000906.
%Y A000457 Third column of triangle A001497.
%Y A000457 Second column (m=1) of unsigned Laguerre-Sonin a=1/2 triangle |A130757|.
%Y A000457 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 
               2009: (Start)
%Y A000457 Cf. A160473.
%Y A000457 (End)
%Y A000457 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 16 
               2009: (Start)
%Y A000457 Equals row sums of A163939.
%Y A000457 (End)
%Y A000457 Sequence in context: A046715 A079515 A024131 this_sequence A113348 A068883 
               A087599
%Y A000457 Adjacent sequences: A000454 A000455 A000456 this_sequence A000458 A000459 
               A000460
%K A000457 nonn,easy
%O A000457 0,2
%A A000457 N. J. A. Sloane (njas(AT)research.att.com).
%E A000457 More terms from Sascha Kurz (sascha.kurz(AT)uni-bayreuth.de), Aug 15 
               2002

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