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A071723 Expansion of (1+x^2*C^2)*C^4, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108. 0
1, 4, 15, 54, 192, 682, 2431, 8710, 31382, 113696, 414086, 1515516, 5571750, 20569590, 76228095, 283481670, 1057628550, 3957577800, 14849601090, 55859886420, 210622646520, 795898303668, 3013646759910, 11432740177564, 43448822603452, 165396657221152 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = (Sum_{k=0..n} (k+1)*(k^2+k+1)*binomial(2*n-k,n))/(n+1). - Vladimir Kruchinin, Sep 28 2011

PROG

(Maxima) a(n):=sum((k+1)*(k^2+k+1)*binomial(2*n-k, n), k, 0, n)/(n+1); /* Vladimir Kruchinin, Sep 28 2011 */

CROSSREFS

Sequence in context: A291032 A006234 A094821 * A001559 A002311 A102349

Adjacent sequences:  A071720 A071721 A071722 * A071724 A071725 A071726

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 06 2002

STATUS

approved

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Last modified September 19 21:42 EDT 2020. Contains 337184 sequences. (Running on oeis4.)