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Search: id:A001514
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| A001514 |
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Bessel polynomial {y_n}'(1).
(Formerly M4654 N1993)
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+0
11
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| 0, 1, 9, 81, 835, 9990, 137466, 2148139, 37662381, 733015845, 15693217705, 366695853876, 9289111077324, 253623142901401, 7425873460633005, 232122372003909045, 7715943399320562331, 271796943164015920914, 10114041937573463433966
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 77.
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LINKS
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Index entries for sequences related to Bessel functions or polynomials
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FORMULA
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(1/2) * Sum((n+k+2)!/((n-k)!*k!*2^k),k=0..n) (with a different offset).
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MAPLE
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(As in A001497 define:) f := proc(n) option remember; if n <=1 then (1+x)^n else expand((2*n-1)*x*f(n-1)+f(n-2)); fi; end;
[seq( subs(x=1, diff(f(n), x)), n=0..60)];
f2:=proc(n) local k; add((n+k+2)!/((n-k)!*k!*2^k), k=0..n); end; [seq(f2(n), n=0..60)]; # uses a different offset
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CROSSREFS
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Cf. A001515, A001516, A001518, A065920, A144505.
Sequence in context: A101601 A144821 A137062 this_sequence A077364 A067478 A077486
Adjacent sequences: A001511 A001512 A001513 this_sequence A001515 A001516 A001517
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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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