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

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A172383 a(0)=1, otherwise a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-k-1,k)*a(n-1-2*k). 2
 1, 1, 1, 2, 4, 8, 19, 46, 118, 322, 903, 2653, 8053, 25194, 81387, 269667, 917529, 3197480, 11393821, 41497060, 154186653, 584151512, 2254240317, 8852998343, 35361762709, 143540660088 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS FORMULA G.f. A(x) satisfies: A(x) = 1 + (x/(1-x^2)) * A(x/(1-x^2)). EXAMPLE Eigensequence for number triangle   1;   1,  0;   0,  1,  0;   1,  0,  1,  0;   0,  2,  0,  1,  0;   1,  0,  3,  0,  1,  0;   0,  3,  0,  4,  0,  1,  0;   1,  0,  6,  0,  5,  0,  1,  0;   0,  4,  0, 10,  0,  6,  0,  1,  0;   1,  0, 10,  0, 15,  0,  7,  0,  1,  0;   0,  5,  0, 20,  0, 21,  0,  8,  0,  1,  0; (augmented version of Riordan array (1/(1-x^2), x/(1-x^2)), A030528. MAPLE A172383 := proc(n)     option remember;     if n = 0 then         1;     else         add(binomial(n-k-1, k)*procname(n-1-2*k), k=0..floor((n-1)/2)) ;     end if; end proc: seq(A172383(n), n=0..20) ; # R. J. Mathar, Feb 11 2015 MATHEMATICA a[n_]:= If[n == 0, 1, Sum[Binomial[n-k-1, k]*a[n-2*k-1], {k, 0, Floor[(n-1)/2]}]]; Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 07 2018 *) CROSSREFS Cf. A030528. Sequence in context: A151526 A099526 A005703 * A003081 A100133 A099598 Adjacent sequences:  A172380 A172381 A172382 * A172384 A172385 A172386 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 01 2010 EXTENSIONS Name corrected by R. J. Mathar, Feb 11 2015 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 December 5 09:45 EST 2021. Contains 349543 sequences. (Running on oeis4.)