A095177 -id:A095177 - cp's OEIS frontend

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

N. J. A. Sloane and Simon Plouffe

nonn

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).

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.

Same as 24*A095177.

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

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

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

Error in description corrected Jan 30 2008

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

A095740 E.g.f.: exp(x)/(1-x)^9.

Original entry on oeis.org

1, 10, 109, 1288, 16417, 224686, 3288205, 51263164, 848456353, 14862109042, 274743964621, 5346258202000, 109249238631169, 2339328151461718, 52384307381414317, 1224472783033479556, 29826054965115774145

Offset: 0

Philippe Deléham Jul 09 2004

nonn

Sum_{k = 0..n} A094816(n,k)*x^k gives A000522(n), A001339(n), A082030(n), A095000(n), A095177(n), A096307(n), A096341(n), A095722(n) for x = 1, 2, 3, 4, 5, 6, 7, 8.

Robert Israel, Table of n, a(n) for n = 0..440

seq(simplify(hypergeom([9,-n],[],-1)),n=0..30); # Robert Israel, May 27 2016

Table[HypergeometricPFQ[{9, -n}, {}, -1], {n, 0, 20}] (* Benedict W. J. Irwin, May 27 2016 *)

a(n) = Sum_{k = 0..n} A094816(n, k)*9^k.
a(n) = Sum_{k = 0..n} binomial(n, k)*(k+8)!/8!.
a(n) = 2F0(9,-n;;-1). - Benedict W. J. Irwin, May 27 2016
a(n) = ((n^8 + 28*n^7 + 350*n^6 + 2492*n^5 + 10899*n^4 + 29596*n^3 + 48082*n^2 + 42048*n + 14833) * Gamma(n+1,1)*e + n^7 + 28*n^6 + 349*n^5 + 2465*n^4 + 10579*n^3 + 27501*n^2 + 40132*n + 25487) / 40320. - Robert Israel, May 27 2016

cp's OEIS Frontend

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

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