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 A099021 Main diagonal of array in A099020. 2
 1, 1, 4, 24, 198, 2070, 26160, 387240, 6565020, 125341020, 2659925520, 62089917120, 1580632348680, 43571319671880, 1292731109429760, 41068078953501600, 1390717740470058000, 50003952605673066000, 1902359109096675028800, 76341746199227491382400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Diagonal of Euler-Seidel matrix with start sequence A001147. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..150 FORMULA a(n) = (1/(sqrt(2*Pi)))*Int(exp(-x^2/2)*(x(1+x))^n,x,-infinity,infinity). - Paul Barry, Apr 19 2010 Contribution from Vaclav Kotesovec, Oct 14 2012: (Start) E.g.f.: exp(x^2/(2-4*x))/sqrt(1-2*x). Recurrence: a(n) = (4*n-3)*a(n-1) - (n-1)*(4*n-7)*a(n-2) - (n-2)*(n-1)*a(n-3). a(n) ~ 2^(n-1/2)*exp(sqrt(n/2)-n-3/16)*n^n. (End) MAPLE a:= proc(n) a(n):= `if`(n<3, [1, 1, 4][n+1], (4*n-3)*a(n-1) -(n-1)*(4*n-7)*a(n-2) -(n-2)*(n-1)*a(n-3)) end: seq (a(n), n=0..20); # Alois P. Heinz, Oct 20 2012 MATHEMATICA Table[n!*SeriesCoefficient[E^(x^2/(2-4*x))/Sqrt[1-2*x], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *) CROSSREFS Sequence in context: A101370 A201338 A362355 * A220690 A136229 A138419 Adjacent sequences: A099018 A099019 A099020 * A099022 A099023 A099024 KEYWORD nonn AUTHOR Ralf Stephan, Sep 23 2004 STATUS approved

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Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)