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A129833
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a(n) = sum_{k = 0..n } binomial(n + 1, k + 1)*binomial(n, k)*k!.
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0
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1, 3, 11, 52, 309, 2221, 18703, 180216, 1952457, 23466223, 309577971, 4444537868, 68948023741, 1148825560377, 20455144724407, 387479309532976, 7778881684953873, 164942847995071611, 3682885668837002587
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Suggested by A052852 (stalactic classes of endofunctions) with n replaced by n+1 in the binomial coefficients.
A052852 is: g[n_] = Sum[Binomial[n - 1, k - 1]*Binomial[n, k]*k!, {k, 0, n}] A straight shift function is: f[n_]=Sum[Binomial[n + 1, k + 1]*Binomial[n, k]*(k + 1)!, {k, 0, n}]
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REFERENCES
| F. Hivert, J.-C. Novelli and J.-Y. Thibon, Commutative combinatorial Hopf algebras.
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MATHEMATICA
| f[n_] = Sum[Binomial[n + 1, k + 1]*Binomial[n, k]*k!, {k, 0, n}]; Table[f[n], {n, 1, 20}]
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CROSSREFS
| Cf. A052852.
Sequence in context: A014510 A058799 A054362 * A107958 A053557 A039302
Adjacent sequences: A129830 A129831 A129832 * A129834 A129835 A129836
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 21 2007
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 30 2007
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