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A036910 a(n) = (binomial(4*n, 2*n) + binomial(2*n, n)^2)/2. 5
1, 5, 53, 662, 8885, 124130, 1778966, 25947612, 383358645, 5719519850, 85990654178, 1300866635172, 19780031677718, 302045506654052, 4629016098160220, 71163013287905912, 1096960888092571317, 16949379732631632570, 262435310495071434602 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

The right-hand side of a binomial coefficient identity in H. W. Gould, Combinatorial Identities, Morgantown, 1972, Eq 3.68, page 30.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{k=0..n} binomial(2n, k)^2. - Paul Barry, May 15 2003

From G. C. Greubel, Dec 09 2021: (Start)

a(n) = A000984(2*n) + A000984(n)^2.

a(n) = A001448(n) + A000984(n)^2.

a(n) = (1/2)*Sum_{k=0..n} A157531(n, k).

G.f.: sqrt(1 + sqrt(1 - 16*x))/(2*sqrt(2)*sqrt(1 - 16*x)) + (1/Pi)*EllipticK[16*x]. (End)

MATHEMATICA

B[n_] := Binomial[2*n, n]/2; Table[B[2*n] + 2*B[n]^2, {n, 0, 40}] (* G. C. Greubel, Dec 09 2021 *)

PROG

(MAGMA) [(Binomial(4*n, 2*n) + Binomial(2*n, n)^2)/2: n in [0..40]]; // G. C. Greubel, Dec 09 2021

(Sage) [(binomial(4*n, 2*n) + binomial(2*n, n)^2)/2 for n in (0..40)] # G. C. Greubel, Dec 09 2021

(PARI) a(n) = (binomial(4*n, 2*n)+binomial(2*n, n)^2)/2; \\ Michel Marcus, Dec 09 2021

CROSSREFS

Cf. A000984, A001448, A157531.

Sequence in context: A186206 A123788 A333096 * A235371 A036916 A118583

Adjacent sequences:  A036907 A036908 A036909 * A036911 A036912 A036913

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 20 13:02 EDT 2022. Contains 353873 sequences. (Running on oeis4.)