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 A294573 a(n) = n! * [x^n] exp((n+1)*x)*BesselI(1,2*x)/x. 1
 1, 2, 10, 76, 777, 9996, 155139, 2821400, 58856963, 1385621260, 36343079188, 1051024082472, 33226817252215, 1140040324751160, 42193259673938754, 1675570154136359472, 71069261432474378715, 3206616936773061141900, 153358034674756782660342, 7749560706936442485607560 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The n-th term of the n-th binomial transform of A001006. LINKS Robert Israel, Table of n, a(n) for n = 0..300 N. J. A. Sloane, Transforms FORMULA a(n) = [x^n] (1 - (n + 1)*x - sqrt((1 - (n - 1)*x)*(1 - (n + 3)*x)))/(2*x^2). a(n) ~ exp(1) * BesselI(1,2) * n^n. - Vaclav Kotesovec, Nov 13 2017 MAPLE S:= series(exp((n+1)*x)*BesselI(1, 2*x)/x, x, 102): seq(simplify(n!*coeff(S, x, n)), n=0..100); # Robert Israel, Nov 03 2017 MATHEMATICA Table[n! SeriesCoefficient[Exp[(n + 1) x] BesselI[1, 2 x]/x, {x, 0, n}], {n, 0, 19}] Table[SeriesCoefficient[(1 - (n + 1) x - Sqrt[(1 - (n - 1) x) (1 - (n + 3) x)])/(2 x^2), {x, 0, n}], {n, 0, 19}] Table[(n + 1)^n HypergeometricPFQ[{1/2 - n/2, -n/2}, {2}, 4/(n + 1)^2], {n, 0, 19}] CROSSREFS Diagonal of A247495. Cf. A001006, A247496. Sequence in context: A088500 A295929 A195136 * A301741 A140763 A245307 Adjacent sequences:  A294570 A294571 A294572 * A294574 A294575 A294576 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Nov 02 2017 STATUS approved

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Last modified October 21 11:15 EDT 2019. Contains 328294 sequences. (Running on oeis4.)