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Search: id:A100524
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| A100524 |
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Sum((-1)^(n-k)*binomial(n,k)*bell(k), k=0..n)*sum((k-1)!*binomial(n-1,k-1)*binomial(n,k-1),k=1..n). |
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+0
1
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| 0, 3, 13, 292, 5511, 166091, 6096546, 281962395, 15743194025, 1044554014702, 80967658322673, 7236647136567861, 737470098999168640, 84879860776191764271, 10943491685936397689965, 1569258830662933925039980
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Arises in combinatorial field theory.
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REFERENCES
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P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Some useful combinatorial formulas for bosonic operators, J. Math. Phys. 46, 052110 (2005) (6 pages).
P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G E. H. Duchamp, Combinatorial field theories via boson normal ordering, preprint, Apr 27 2004.
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LINKS
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P. Blasiak, K. A. Penson, A. I. Solomon, A. Horzela and G. E. H. Duchamp, Combinatorial field theories via boson normal ordering
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FORMULA
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a(n)=sum((-1)^(n-k)*binomial(n, k)*bell(k), k=0..n)*sum((k-1)!*binomial(n-1, k-1)*binomial(n, k-1), k=1..n): a(n)=A000296(n)*A000262(n)
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MAPLE
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with(combinat): A:=n->sum((-1)^(n-k)*binomial(n, k)*bell(k), k=0..n)*sum((k-1)!*binomial(n-1, k-1)*binomial(n, k-1), k=1..n): 0, seq(A(n), n=2..18);
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CROSSREFS
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Cf. A000262, A000296.
Adjacent sequences: A100521 A100522 A100523 this_sequence A100525 A100526 A100527
Sequence in context: A042823 A132560 A128385 this_sequence A000859 A045748 A113526
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 24 2004
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