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Search: id:A083886
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| A083886 |
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Expansion of exp(3x)exp(x^2). |
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+0
2
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| 1, 3, 11, 45, 201, 963, 4899, 26253, 147345, 862083, 5238459, 32957037, 214117209, 1433320515, 9867008979, 69734001357, 505212273441, 3747124863747, 28418591888235, 220152270759597, 1740363304031721, 14027180742479043
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A000898.
Hankel transform is A108400. [From Paul Barry (pbarry(AT)wit.ie), Jun 13 2009]
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FORMULA
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E.g.f.: exp(3x+x^2).
Contribution from Paul Barry (pbarry(AT)wit.ie), Jun 13 2009: (Start)
G.f.: 1/(1-3x-2x^2/(1-3x-4x^2/(1-3x-6x^2/(1-3x-8x^2/(1-... (continued fraction);
a(n)=sum{k=0..floor(n/2), C(n,2k)(2k)!3^(n-2k)/k!}. (End)
a(n)=i^n*Hermite_H(n, -3i/2), i=sqrt(-1). [From Paul Barry (pbarry(AT)wit.ie), Jun 15 2009]
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CROSSREFS
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Cf. A047974, A001813.
Sequence in context: A151131 A151132 A151133 this_sequence A030866 A030941 A030918
Adjacent sequences: A083883 A083884 A083885 this_sequence A083887 A083888 A083889
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 09 2003
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