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 A136557 a(n) = Sum_{k=0..n} binomial(2^k + n-k-1, k). 3
 1, 2, 6, 45, 1436, 171836, 68149425, 89431630740, 396956313475102, 6099399658235428041, 331007760926212498510464, 64484289650612910347505873728, 45677712418497545460138258802186905 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..50 FORMULA Equals antidiagonal sums of square array A136555. G.f.: A(x) = Sum_{n>=0} (1+2^n*x)^-1 * (1-x-2^n*x^2)^-1 * log(1+2^n*x)^n / n!. a(n) ~ 2^(n^2) / n!. - Vaclav Kotesovec, Jul 02 2016 MAPLE A136557:= n-> add(binomial(2^k +n-k-1, k), k=0..n); seq(A136557(n), n=0..20); # G. C. Greubel, Mar 15 2021 MATHEMATICA Table[Sum[Binomial[2^k+n-k-1, k], {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Jul 02 2016 *) PROG (PARI) a(n)=sum(k=0, n, binomial(2^k+n-k-1, k)) (PARI) /* As coefficient of x^n in the g.f.: */ {a(n)=polcoeff(sum(i=0, n, ((1+2^i*x+x*O(x^n))*(1-x-2^i*x^2))^-1*log(1+2^i*x+x*O(x^n))^i/i!), n)} (Sage) [sum(binomial(2^k +n-k-1, k) for k in (0..n)) for n in (0..20)] # G. C. Greubel, Mar 15 2021 (Magma) [(&+[Binomial(2^k +n-k-1, k): k in [0..n]]): n in [0..20]]; // G. C. Greubel, Mar 15 2021 CROSSREFS Cf. A136555, A136556. Sequence in context: A347984 A229836 A359659 * A092662 A052811 A078603 Adjacent sequences: A136554 A136555 A136556 * A136558 A136559 A136560 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 07 2008 STATUS approved

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Last modified October 1 22:38 EDT 2023. Contains 365828 sequences. (Running on oeis4.)