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A137646 a(n) = Sum_{k=0..n} C(k*(k+1)/2, k) * C(k*(k+1)/2, n-k). 1
1, 1, 4, 29, 339, 5406, 109159, 2664399, 76219485, 2499425650, 92402751894, 3801481338219, 172231146665554, 8520038462375370, 456913020454609665, 26402792230144908683, 1635399597258002744628, 108090275300425856404653 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..364

MAPLE

f:= proc(n) add(binomial(k*(k+1)/2, k)*binomial(k*(k+1)/2, n-k), k=ceil((sqrt(8*n+9)-3)/2)..n) end proc:

map(f, [$0..20]); # Robert Israel, Jun 07 2018

MATHEMATICA

Join[{1}, Table[Sum[Binomial[(k(k+1))/2, k]Binomial[(k(k+1))/2, n-k], {k, n}], {n, 20}]] (* Harvey P. Dale, Jul 09 2018 *)

PROG

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

CROSSREFS

Sequence in context: A305636 A276728 A256006 * A231498 A168602 A000798

Adjacent sequences:  A137643 A137644 A137645 * A137647 A137648 A137649

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 31 2008

STATUS

approved

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Last modified December 6 14:44 EST 2019. Contains 329806 sequences. (Running on oeis4.)