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A130713 a(0)=a(2)=1, a(1)=2, a(n)=0 for n > 2. 3
1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Self-convolution of A019590. Up to a sign the convolutional inverse of the natural numbers sequence. - Tanya Khovanova, Jul 14 2007
Iterated partial sums give the chain A130713 -> A113311 -> A008574 -> A001844 -> A005900 -> A006325 -> A033455 -> A259181, up to index. The k-th term of the n-th partial sums is (n^2-7n+14 + 4k(k+n-4))(k+n-4)!/(k-1)!/(n-1)!, for k > 3-n. Iterating partial sums in reverse (n-th differences with n zeros prepended) gives row (n+3) of A182533, modulo signs and trailing zeros. - Travis Scott, Feb 19 2023
LINKS
FORMULA
G.f.: 1 + 2*x + x^2.
a(n) = binomial(2n, n^2). - Wesley Ivan Hurt, Mar 08 2014
MAPLE
A130713:=n->binomial(2*n, n^2); seq(A130713(n), n=0..100); # Wesley Ivan Hurt, Mar 08 2014
MATHEMATICA
Table[Binomial[2 n, n^2], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 08 2014 *)
CROSSREFS
Sequence in context: A230093 A033322 A329679 * A236619 A355627 A300828
KEYWORD
easy,nonn
AUTHOR
Paul Curtz and Tanya Khovanova, Jul 01 2007
STATUS
approved

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Last modified June 14 21:35 EDT 2024. Contains 373401 sequences. (Running on oeis4.)