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

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

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->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.

Adjacent sequences: A000020 A000021 A000022 this_sequence A000024 A000025 A000026

Sequence in context: A037223 A066988 A100384 this_sequence A010584 A131659 A137726

sign

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