A110531 Recurrence: a(n) = Sum_{k=0..n-1} C(2*n-1,n-k-1)*a(k) with a(0)=1.

1, 1, 4, 19, 103, 628, 4258, 31753, 257815, 2259718, 21230800, 212579938, 2257364371, 25315773751, 298758986356, 3698444546248, 47893544997832, 647174968407262, 9105301419381562, 133116659482393549

Offset

0,3

Links

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

Example

a(1) = 1*1 = 1,
a(2) = 3*1 + 1*1 = 4,
a(3) = 10*1 + 5*1 + 1*4 = 19,
a(4) = 35*1 + 21*1 + 7*4 + 1*19 = 103,
a(5) = 126*1 + 84*1 + 36*4 + 9*19 + 1*103 = 628.
This sequence can be generated by the addition table:
__1__(1)__1___1___1___1 ...
__1___2___3__(4)__5___6___7 ...
__4___5___7__10__14_(19)_25___32 ...
_19__23__28__35__45__59__78_(103)_135 ...
103_122_145_173_208_253_312__390__493_(628) ...

Mathematica

nmax = 30; aa = ConstantArray[0, nmax+1]; aa[[1]] = 1; Do[aa[[n+1]]=Sum[Binomial[2*n-1, 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-1, n-k-1)*a(k)))

Crossrefs

Cf. A110530.

Sequence in context: A199876 A225029 A078940 * A367808 A276975 A178302

Adjacent sequences: A110528 A110529 A110530 * A110532 A110533 A110534

Keyword

nonn

Author

Paul D. Hanna, Jul 25 2005

Status

approved