A110530 Recurrence: a(n) = Sum_{k=0..n-1} C(2*n-2,n-k-1)*a(k) with a(0)=1.

1, 1, 3, 13, 66, 380, 2447, 17424, 135740, 1146202, 10409616, 101031397, 1042361261, 11380543227, 130980176993, 1583726089859, 20058575880505, 265416510500487, 3660581511822798, 52511905732091815, 782044494316086134

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..500

Example

a(1) = 1*1 =1,
a(2) = 2*1 + 1*1 = 3,
a(3) = 6*1 + 4*1 + 1*3 = 13,
a(4) = 20*1 + 15*1 + 6*3 + 1*13 = 66,
a(5) = 70*1 + 56*1 + 28*3 + 8*13 + 1*66 = 380.
This sequence can be generated by the addition table:
(1)_1__1___1___1 ...
_1__2_(3)__4___5___6 ...
_3__4__6___9_(13)_18__24 ...
13_16_20__26__35__48_(66)_90 ...
66_79_95_115_141_176_224_290_(380) ...

Mathematica

nmax = 30; aa = ConstantArray[0, nmax+1]; aa[[1]] = 1; Do[aa[[n+1]]=Sum[Binomial[2*n-2, n-k-1]*aa[[k+1]], {k, 0, n-1}], {n, 1, nmax}]; aa (* Vaclav Kotesovec, May 06 2015 , much faster than PARI *)

Prog

(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(2*n-2, n-k-1)*a(k)))

Crossrefs

Cf. A110531.

Sequence in context: A112807 A219537 A045743 * A142979 A302303 A201713

Adjacent sequences: A110527 A110528 A110529 * A110531 A110532 A110533

Keyword

nonn

Author

Paul D. Hanna, Jul 25 2005

Status

approved