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 A136638 a(n) = Sum_{k=0..[n/2]} C(n-k, k) * C(3^(n-2*k)*2^k, n-k). 3
 1, 3, 38, 2955, 1666194, 6775599252, 204212962736426, 47025953519744215608, 84798028785462127288681736, 1219731316443261012339196962784452, 141916030637329352970764084182705691263552 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Equals antidiagonal sums of triangle A136635. LINKS FORMULA G.f.: A(x) = Sum_{n>=0} log(1 + 3^n*x + 2^n*x^2)^n / n!. a(n) ~ 3^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016 EXAMPLE More generally, if Sum_{n>=0} log(1 + b*p^n*x + d*q^n*x^2)^n/n! = Sum_{n>=0} a(n)*x^n then a(n) = Sum_{k=0..[n/2]} C(n-k,k)*b^(n-2k)*d^k*C(p^(n-2k)*q^k,n-k). MATHEMATICA Table[Sum[Binomial[n-k, k]*Binomial[2^k*3^(n-2*k), n-k], {k, 0, Floor[n/2]}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *) PROG (PARI) {a(n)=sum(k=0, n\2, binomial(n-k, k)*binomial(3^(n-2*k)*2^k, n-k))} (PARI) /* Using g.f.: */ {a(n)=polcoeff(sum(i=0, n, log(1+3^i*x+2^i*x^2)^i/i!), n, x)} CROSSREFS Cf. A136635 (triangle), A014070 (main diagonal), A136393 (column 0), A136636 (column 1), A136637 (row sums). Sequence in context: A278927 A099022 A229365 * A213002 A213003 A213004 Adjacent sequences:  A136635 A136636 A136637 * A136639 A136640 A136641 KEYWORD nonn AUTHOR Vladeta Jovovic and Paul D. Hanna, Jan 15 2008 STATUS approved

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Last modified December 6 08:53 EST 2019. Contains 329788 sequences. (Running on oeis4.)