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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A051163 Sequence is defined by property that (a0,a1,a2,a3,...) = binomial transform of (a0,a0,a1,a1,a2,a2,a3,a3,...). 8
 1, 2, 5, 12, 30, 76, 194, 496, 1269, 3250, 8337, 21428, 55184, 142376, 367916, 952000, 2466014, 6393372, 16586678, 43054344, 111801908, 290412296, 754543052, 1960808160, 5096293794, 13247503540, 34440553562, 89549255592, 232868582328, 605646682144 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals the self-convolution of A027826. Also equals antidiagonal sums of symmetric square array A100936. - Paul D. Hanna, Nov 22 2004 Equals eigensequence of triangle A152198. - Gary W. Adamson, Nov 28 2008 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 N. J. A. Sloane, Transforms FORMULA a(n) = 1 + Sum_{k=1..n} Sum_{j=0..n-k} C(k, j)*C(n-k, j)*a(j). - Paul D. Hanna, Nov 22 2004 G.f. A(x) satisfies: A(x) = A(x^2/(1-x)^2)/(1-x)^2 and A(x^2) = A(x/(1+x))/(1+x)^2. - Paul D. Hanna, Nov 22 2004 MAPLE a:= proc(n) option remember; add(`if`(k<2, 1,       a(iquo(k, 2)))*binomial(n, k), k=0..n)     end: seq(a(n), n=0..40);  # Alois P. Heinz, Jul 08 2015 MATHEMATICA a[n_] := a[n] = 1 + Sum[Binomial[k, j]*Binomial[n-k, j]*a[j], {k, 1, n}, {j, 0, n-k}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Nov 11 2015 *) PROG (PARI) a(n)=1+sum(k=1, n, sum(j=0, n-k, binomial(k, j)*binomial(n-k, j)*a(j))) (PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=2; A=subst(A, x, (x/(1-x))^2)/(1-x)); polcoeff(A^2, n)) for(n=0, 40, print1(a(n), ", ")) \\ Paul D. Hanna, Nov 22 2004 CROSSREFS Cf. A051164, A051165, A051166, A027826, A100936, A100937, A152198. Sequence in context: A092247 A331233 A108360 * A051450 A038508 A105695 Adjacent sequences:  A051160 A051161 A051162 * A051164 A051165 A051166 KEYWORD easy,nonn,eigen AUTHOR EXTENSIONS More terms from Vladeta Jovovic, Jul 26 2002 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 August 6 10:14 EDT 2020. Contains 336245 sequences. (Running on oeis4.)