A132428 Central terms of triangle A132427.

1, 1, 3, 10, 43, 216, 1241, 7988, 56763, 440254, 3693728, 33281359, 320112326, 3270177860, 35329070470, 402128329243, 4806784533967, 60166803598106, 786622663286330, 10717555856584617, 151864784070048105

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

Binomial transform equals A125273.

a(n)=sum(k=1..n, sum(i=k..n, binomial(i-1,k-1)*binomial(i,n-i))*a(k-1)), n>0,a(0)=1. [Vladimir Kruchinin, May 02 2012]

Prog

(PARI) {a(n)=local(G=1+x+x*O(x^n)); for(i=0, n, G=1+x*subst(G, x, x/(1-x)^2)/(1-x)); polcoeff(subst((G-1)/x, x, x/(1+x))/(1+x), n)}
(Maxima) a(n):=if n=0 then 1  else sum(sum(binomial(i-1, k-1)*binomial(i, n-i), i, k, n)*a(k-1), k, 1, n); [Vladimir Kruchinin, May 02 2012]

Crossrefs

Cf. A125273; A132427.

Sequence in context: A205487 A323667 A030935 * A030890 A030833 A318372

Adjacent sequences: A132425 A132426 A132427 * A132429 A132430 A132431

Keyword

nonn,tabl

Author

Paul D. Hanna, Aug 21 2007

Status

approved