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A086621 Main diagonal of square table A086620 of coefficients, T(n,k), of x^n*y^k in f(x,y) that satisfies f(x,y) = 1/(1-x-y) + xy*f(x,y)^2. 3
1, 3, 14, 79, 504, 3514, 26172, 204831, 1664696, 13930840, 119312544, 1041227642, 9228614836, 82867255956, 752405060536, 6897376441167, 63760133568096, 593763928313128, 5565678569009328, 52475976165495960, 497376657383374560, 4736680863568248480, 45304174896889357440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{j=0..n} binomial(n,j) * binomial(2*n-j,n) * binomial(2*j,j)/(j+1). - Andrew Howroyd, Apr 11 2021

PROG

(PARI) a(n) = {sum(j=0, n, binomial(n, j)*binomial(2*n-j, n)*binomial(2*j, j)/(j+1))} \\ Andrew Howroyd, Apr 11 2021

CROSSREFS

Cf. A086620 (table), A086622 (antidiagonal sums).

Sequence in context: A330074 A059276 A003169 * A020089 A218677 A305128

Adjacent sequences:  A086618 A086619 A086620 * A086622 A086623 A086624

KEYWORD

nonn,changed

AUTHOR

Paul D. Hanna, Jul 24 2003

EXTENSIONS

Terms a(18) and beyond from Andrew Howroyd, Apr 11 2021

STATUS

approved

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Last modified April 22 19:11 EDT 2021. Contains 343177 sequences. (Running on oeis4.)