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A128321 Column 0 of triangle A128320. 4
1, 1, 4, 17, 98, 622, 4512, 35373, 300974, 2722070, 26118056, 263266346, 2780054884, 30586452652, 349724463584, 4141218303165, 50678688359190, 639387728054310, 8302396672724280, 110754894628585950 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n) = Sum_{k=0..[n/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n,2k) where A000108 is the Catalan numbers. a(n) = Sum_{k=0..[(n+1)/2]} C(2(n-k),n-k)/(n-k+1)*C(2k,k)/(k+1)*(k+1)!*C(n,2k).

PROG

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

CROSSREFS

Cf. A128320 (triangle), A128322 (column 1), A128323 (column 2), A128324 (row sums); variant: A115081.

Sequence in context: A278644 A249078 A024052 * A290352 A091635 A306160

Adjacent sequences:  A128318 A128319 A128320 * A128322 A128323 A128324

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Feb 25 2007

STATUS

approved

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)