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A102773
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Sum_{i=0..n} C(n,i)^2*i!*4^i.
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3
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1, 5, 49, 709, 13505, 318181, 8916145, 289283429, 10656031489, 439039941445, 19995858681521, 997184081617285, 54026137182982849, 3159127731435043109, 198258247783634075185, 13289190424904891606821, 947419111092028780186625
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| Z. Li, Z. Li and Y. Cao, Enumeration of symplectic and orthogonal injective partial transformations, Discrete Math., 306 (2006), 1781-1787. (The function s_n.)
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FORMULA
| E.g.f. = (1/(1-4x))*exp(x/(1-4x))
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MAPLE
| seq(sum('binomial(k, i)^2*i!*4^i', 'i'=0..k), k=0..30);
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MATHEMATICA
| f[n_] := Sum[k!*4^k*Binomial[n, k]^2, {k, 0, n}]; Table[ f[n], {n, 0, 16}] (* or *)
Range[0, 16]! CoefficientList[ Series[1/(1 - 4x)*Exp[x/(1 - 4x)], {x, 0, 16}], x] (from Robert G. Wilson v Mar 16 2005)
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CROSSREFS
| Cf. A002720, A025167.
Sequence in context: A089914 A052142 A136729 * A028575 A006554 A052750
Adjacent sequences: A102770 A102771 A102772 * A102774 A102775 A102776
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KEYWORD
| easy,nonn
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AUTHOR
| Miklos Kristof (kristmikl(AT)freemail.hu), Mar 16 2005
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 16 2005
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