The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A003470 a(n) = n*a(n-1) - a(n-2) + 1 + (-1)^n. (Formerly M2759) 10
 1, 1, 3, 8, 31, 147, 853, 5824, 45741, 405845, 4012711, 43733976, 520795003, 6726601063, 93651619881, 1398047697152, 22275111534553, 377278848390249, 6768744159489931, 128228860181918440, 2557808459478878871, 53585748788874537851, 1176328664895760953853 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums of A086764. - Philippe Deléham, Apr 27 2004 a(n+2m) == a(n) (mod m) for all n and m. - Robert Israel, Dec 06 2016 REFERENCES 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 John Riordan and N. J. A. Sloane, Correspondence, 1974 FORMULA Diagonal sums of reverse of permutation triangle A008279. a(n) = Sum_{k=0..floor(n/2)} (n-k)!/k!. - Paul Barry, May 12 2004 a(n) = Sum_{k=0..floor(n/2)} C(n-k,k)*(n-2k)!. - Paul Barry Dec 15 2010 G.f.: 1/(1-x^2-x/(1-x/(1-x^2-2x/(1-2x/(1-x^2-3x/(1-3x/(1-x^2-4x/(1-4x/(1-.... (continued fraction); G.f.: 1/(1-x-x^2-x^2/(1-3x-x^2-4x^2/(1-5x-x^2-9x^2/(1-7x-x^2-16x^2/(1-... (continued fraction). - Paul Barry, Dec 15 2010 G.f.: hypergeom([1,1],[],x/(1-x^2))/(1-x^2). - Mark van Hoeij, Nov 08 2011 G.f.: 1/Q(0), where Q(k)= 1 - x^2 - x*(k+1)/(1-x*(k+1)/Q(k+1)); (continued fraction). - Sergei N. Gladkovskii, Apr 20 2013 From Robert Israel, Dec 06 2016: (Start) a(2m) = hypergeom([1,-m,m+1],[],-1). a(2m+1) = hypergeom([1,-m,m+2],[],-1)*(m+1). a(2m-1) + a(2m+1) = (2m+1) a(2m). (End) 0 = a(n)*(-a(n+2) - a(n+3)) + a(n+1)*(-2 + a(n+1) - 2*a(n+3) + a(n+4)) + a(n+2)*(-2*a(n+3) + a(n+4)) + a(n+3)*(+2 - a(n+3)) if n >= 0. - Michael Somos, Dec 06 2016 0 = a(n)*(-a(n+2) + a(n+4)) + a(n+1)*(+a(n+1) - a(n+2) - a(n+3) + 3*a(n+4) - a(n+5)) + a(n+2)*(-a(n+3) + a(n+4)) + a(n+3)*(-a(n+4) + a(n+5)) + a(n+4)*(-a(n+4)) if n >= 0. - Michael Somos, Dec 06 2016 a(n) = Sum_{k=0..n} (-1)^k*hypergeom([k+1, k-n], [], -1). - Peter Luschny, Oct 05 2017 EXAMPLE G.f. = 1 + x + 3*x^2 + 8*x^3 + 31*x^4 + 147*x^5 + 853*x^6 + 5824*x^7 + ... MAPLE f:= gfun:-rectoproc({a(n) -(n-1)*a(n-1)-(n-2)*a(n-2)+a(n-3)-2=0, a(0)=1, a(1)=1, a(2)=3}, a(n), remember): map(f, [\$0..30]); # Robert Israel, Dec 06 2016 MATHEMATICA t = {1, 1}; Do[AppendTo[t, n*t[[-1]] - t[[-2]] + 1 + (-1)^n], {n, 2, 20}] (* T. D. Noe, Oct 07 2013 *) T[n_, k_] := HypergeometricPFQ[{k+1, k-n}, {}, -1]; Table[Sum[(-1)^k T[n, k], {k, 0, n}], {n, 0, 22}] (* Peter Luschny, Oct 05 2017 *) CROSSREFS Cf. A008279, A072374, A086764, A143409. Sequence in context: A148902 A213092 A108492 * A176304 A180385 A148903 Adjacent sequences:  A003467 A003468 A003469 * A003471 A003472 A003473 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Oct 25 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 06:37 EST 2020. Contains 331033 sequences. (Running on oeis4.)