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 A266526 a(n) = coefficient of x^n*y^(n+1)/n! in Log( Sum_{n>=0} (n + y)^(2*n) * x^n/n! ), for n>=1. 6
 1, 4, 42, 752, 19360, 654912, 27546736, 1388207872, 81621893376, 5488951731200, 415721105434624, 35026876903256064, 3250356630453317632, 329437813126362185728, 36214170617862339840000, 4291812357982293898231808, 545518054282041342531076096, 74032137722410904128877494272, 10684317262536125210489796296704, 1634019721630446295055397683200000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Equals the logarithm of the e.g.f. of A266481. Equals the right border of triangle A266521. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..230 FORMULA a(n) ~ 2^(n - 1/4) * (1 + sqrt(2))^(n - 1/2) * exp((1 - sqrt(2))*n) * n^(n-2). - Vaclav Kotesovec, Mar 20 2024 EXAMPLE E.g.f: A(x) = x + 4*x^2/2! + 42*x^3/3! + 752*x^4/4! + 19360*x^5/5! + 654912*x^6/6! + 27546736*x^7/7! + 1388207872*x^8/8! + 81621893376*x^9/9! + 5488951731200*x^10/10! +... where exponentiation yields the e.g.f. of A266481: exp(A(x)) = 1 + x + 5*x^2/2! + 55*x^3/3! + 993*x^4/4! + 25501*x^5/5! + 857773*x^6/6! + 35850795*x^7/7! + 1795564865*x^8/8! + 104972371417*x^9/9! +...+ A266481(n)*x^n/n! +... which equals Limit_{N->oo} [ Sum_{n>=0} (N + n)^(2*n) * (x/N)^n/n! ]^(1/N). PROG (PARI) {a(n) = n! * polcoeff( polcoeff( log( sum(m=0, n+1, (m + y)^(2*m) *x^m/m! ) +x*O(x^n) ), n, x), n+1, y)} for(n=1, 30, print1(a(n), ", ")) CROSSREFS Cf. A266521, A266481. Sequence in context: A259062 A074768 A295763 * A140055 A221096 A179499 Adjacent sequences: A266523 A266524 A266525 * A266527 A266528 A266529 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 01 2016 STATUS approved

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Last modified August 6 00:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)