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A110531 Recurrence: a(n) = Sum_{k=0..n-1} C(2*n-1,n-k-1)*a(k) with a(0)=1. 2
1, 1, 4, 19, 103, 628, 4258, 31753, 257815, 2259718, 21230800, 212579938, 2257364371, 25315773751, 298758986356, 3698444546248, 47893544997832, 647174968407262, 9105301419381562, 133116659482393549 (list; graph; refs; listen; history; text; internal format)
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 * A276975 A178302 A292098

Adjacent sequences:  A110528 A110529 A110530 * A110532 A110533 A110534

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 25 2005

STATUS

approved

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Last modified November 29 02:45 EST 2020. Contains 338756 sequences. (Running on oeis4.)