0,3

A010843, A000023, A000166, A000142, A000522, A010842, A053486, A053487 are successive binomial transforms with the e.g.f. exp(k*x)/(1-x) and recurrence b(n)=n*b(n-1)+k^n and are related to incomplete gamma functions at k. In this case k=-2, a(n)=n*a(n-1)+(-2)^n.

GAMMA(n+1,k)*exp(k) = Sum_{i=0..n} (-1)^(n-i)*binomial(n,i)*i^(n-i)*(i+k)^i. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 19 2002

a(n) is the permanent of the n X n matrix with -1's on the diagonal and 1's elsewhere . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 15 2003

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 210.

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

A. R. Kr\"auter, Permanenten - Ein kurzer \"Uberblick

A. R. Kr\"auter, \"Uber die Permanente gewisser zirkul\"arer Matrizen...

S. Plouffe, Table for n=0..2429

a(n) = Sum(k=0..n, A008290(n, k)*(-1)^k ). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Dec 15 2003

a(n)=sum{k=0..n, (-2)^(n-k)n!/(n-k)!}=sum{k=0..n, binomial(n, k)k!(-2)^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Aug 26 2004

a(n)=sum_{i=0..n} A008290(i)(-1)^i. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Jan 27 2008

a(n) = abs( exp(-2)*GAMMA(n+1,-2) ) (incomplete Gamma function) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Nov 11 2009]

a:=n->n!*sum(((-2)^(k)/k!), k=0..n): seq(a(n), n=0..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 22 2007

(PARI) a(n)=if(n<0, 0, n!*polcoeff(exp(-2*x+x*O(x^n))/(1-x), n))

Cf. A087891, A008290 A089258.

Sequence in context: A037223 A066988 A100384 this_sequence A010584 A131659 A137726

Adjacent sequences: A000020 A000021 A000022 this_sequence A000024 A000025 A000026

sign

N. J. A. Sloane (njas(AT)research.att.com).