A001342 E.g.f.: 24*exp(x)/(1-x)^5.

24, 144, 984, 7584, 65304, 622704, 6523224, 74542464, 923389464, 12331112784, 176656186584, 2703187857504, 44010975525144, 759759305162544, 13863284116261464, 266629052052953664, 5391260831368104984, 114341673457251051024, 2538207055383516388824

Offset: 0

Author

N. J. A. Sloane and Simon Plouffe

Keywords

• nonn

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• E. Biondi, L. Divieti, and G. Guardabassi, Counting paths, circuits, chains and cycles in graphs: A unified approach, Canad. J. Math. 22 1970 22-35.

Crossrefs

Same as 24*A095177.

Programs

Mathematica

nn = 20; Range[0, nn]! CoefficientList[Series[24*Exp[x]/(1 - x)^5, {x, 0, nn}], x] (* T. D. Noe, Jun 28 2012 *)

PARI

a(n) = n!*polcoeff(24*exp(x+x*O(x^n))/(1-x)^5, n) \\ Christian Krause, Dec 21 2022

Formula

a(n) = floor( n! * (n^4+6*n^3+17*n^2+20*n+9) * exp(1) ). [Mark van Hoeij, Nov 11 2009]

a(n) = Sum_{k=0..n} binomial(n, k)*(k+4)!. - Christian Krause, Dec 21 2022

Extensions

Error in description corrected Jan 30 2008

More terms from N. J. A. Sloane, Jan 30 2008