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 A370106 a(n) = Sum_{k=0..n} (-1)^k * binomial(2*n,k) * binomial(3*n,n-k). 2
 1, 1, -3, -17, -19, 126, 591, 344, -5907, -22373, 2122, 280842, 854063, -810692, -13254552, -31693392, 67250413, 615932985, 1101123015, -4368359919, -28043889894, -33371056204, 254637122506, 1245324193704, 693586015791, -13913192640499 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..25. FORMULA a(n) = [x^n] ( (1-x)^2 * (1+x)^3 )^n. The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x/((1-x)^2*(1+x)^3) ). See A370107. PROG (PARI) a(n) = sum(k=0, n, (-1)^k * binomial(2*n, k)*binomial(3*n, n-k)); CROSSREFS Cf. A234839, A368467. Cf. A370107. Sequence in context: A032923 A018750 A177208 * A147845 A077778 A273420 Adjacent sequences: A370103 A370104 A370105 * A370107 A370108 A370109 KEYWORD sign AUTHOR Seiichi Manyama, Feb 10 2024 STATUS approved

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Last modified May 27 02:41 EDT 2024. Contains 372847 sequences. (Running on oeis4.)