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 A107418 a(n) = C(n+3,3)*C(n+6,6). 1
 1, 28, 280, 1680, 7350, 25872, 77616, 205920, 495495, 1101100, 2290288, 4504864, 8446620, 15193920, 26356800, 44279424, 72299997, 115079580, 179012680, 272734000, 407737330, 599124240, 866502000, 1235052000, 1736791875, 2412056556, 3311225568, 4496726080, 6045343480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Robert Israel, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA G.f.: (20*x^3+45*x^2+18*x+1)/(x-1)^10. - Robert Israel, Feb 24 2017 From Amiram Eldar, Sep 06 2022: (Start) Sum_{n>=0} 1/a(n) = 63*Pi^2 - 124149/200. Sum_{n>=0} (-1)^n/a(n) = 3*Pi^2/2 + 1344*log(2)/5 - 40031/200. (End) EXAMPLE If n=0 then C(0+3,3)*C(0+6,6) = C(3,3)*C(6,6) = 1*1 = 1. If n=8 then C(8+3,3)*C(8+6,6) = C(11,3)*C(14,6) = 165*3003 = 495495. MAPLE seq(binomial(n+3, 3)*binomial(n+6, 6), n=0..100); # Robert Israel, Feb 24 2017 MATHEMATICA a[n_] := Binomial[n + 3, 3] * Binomial[n + 6, 6]; Array[a, 30, 0] (* Amiram Eldar, Sep 06 2022 *) PROG (PARI) for(n=0, 29, print1(binomial(n+3, 3)*binomial(n+6, 6), ", ")) CROSSREFS Cf. A062145. Sequence in context: A126549 A300297 A250649 * A183484 A241621 A027781 Adjacent sequences: A107415 A107416 A107417 * A107419 A107420 A107421 KEYWORD easy,nonn AUTHOR Zerinvary Lajos, May 26 2005 EXTENSIONS Corrected and extended by Rick L. Shepherd, May 27 2005 STATUS approved

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Last modified December 7 22:54 EST 2023. Contains 367662 sequences. (Running on oeis4.)