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 A246509 G.f.: Sum_{n>=0} x^n / (1-3*x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * 3^k * x^k] * [Sum_{k=0..n} C(n,k)^2 * 4^k * x^k]. 1
 1, 4, 26, 200, 1694, 15224, 141972, 1359120, 13264246, 131384536, 1316769196, 13323636208, 135885868780, 1395157192624, 14406117404584, 149489132177440, 1557898906160806, 16297193704008856, 171058624529373116, 1800860588158214960, 19010179617892702404, 201164103801453466896 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA G.f.: Sum_{n>=0} x^n / (1-x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k] * [Sum_{k=0..n} C(n,k)^2 * 3^(n-k) * 4^k * x^k]. G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * Sum_{j=0..k} C(k,j)^2 * 3^(k-j) * 4^j * x^j. G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * 3^(n-k) * Sum_{j=0..k} C(k,j)^2 * 4^j * x^j. a(n) = Sum_{k=0..[n/2]} 4^k * Sum_{j=0..n-2*k} C(n-k, k+j)^2 * C(k+j, j)^2 * 3^j. EXAMPLE G.f.: A(x) = 1 + 4*x + 26*x^2 + 200*x^3 + 1694*x^4 + 15224*x^5 +... PROG (PARI) /* By definition: */ {a(n)=local(A=1); A=sum(m=0, n, x^m/(1-3*x)^(2*m+1) * sum(k=0, m, binomial(m, k)^2 * 3^k * x^k) * sum(k=0, m, binomial(m, k)^2 * 4^k * x^k) +x*O(x^n)); polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) (PARI) /* By a binomial identity: */ {a(n)=local(A=1); A=sum(m=0, n, x^m/(1-x)^(2*m+1) * sum(k=0, m, binomial(m, k)^2 * 3^(m-k) * 4^k * x^k) * sum(k=0, m, binomial(m, k)^2 * x^k) +x*O(x^n)); polcoeff(A, n)} for(n=0, 25, print1(a(n), ", ")) (PARI) /* By a binomial identity: */ {a(n)=polcoeff(sum(m=0, n, x^m*sum(k=0, m, binomial(m, k)^2 * sum(j=0, k, binomial(k, j)^2 * 3^(k-j) * 4^j * x^j)+x*O(x^n))), n)} for(n=0, 25, print1(a(n), ", ")) (PARI) /* By a binomial identity: */ {a(n)=polcoeff(sum(m=0, n, x^m*sum(k=0, m, binomial(m, k)^2 * 3^(m-k) * sum(j=0, k, binomial(k, j)^2 * 4^j * x^j)+x*O(x^n))), n)} for(n=0, 25, print1(a(n), ", ")) (PARI) /* Formula for a(n): */ {a(n)=sum(k=0, n\2, sum(j=0, n-2*k, 4^k * binomial(n-k, k+j)^2 * binomial(k+j, j)^2 * 3^j))} for(n=0, 25, print1(a(n), ", ")) CROSSREFS Cf. A246510, A246423. Sequence in context: A278393 A192499 A271935 * A253255 A141381 A118971 Adjacent sequences:  A246506 A246507 A246508 * A246510 A246511 A246512 KEYWORD nonn AUTHOR Paul D. Hanna, Aug 27 2014 STATUS approved

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Last modified August 8 05:50 EDT 2020. Contains 336290 sequences. (Running on oeis4.)