A295099 -id:A295099 - cp's OEIS frontend

A295098 a(n) = n! * [x^n] exp(nx)(1 + exp(x^2/2)x(1 + sqrt(Pi/2)*erf(x/sqrt(2)))).

1, 2, 10, 75, 760, 9715, 150060, 2719017, 56556480, 1328337117, 34773226340, 1003998156293, 31696623421488, 1086258754644505, 40161805428662876, 1593475984997421525, 67534151717002711296, 3044989873158805787409, 145537456143562934305860, 7350253384336351186239341, 391132792671917087054081200

Offset: 0

Ilya Gutkovskiy, Nov 14 2017

nonn

The n-th term of the n-th binomial transform of A006882.

G. C. Greubel, Table of n, a(n) for n = 0..250
N. J. A. Sloane, Transforms
Index entries for sequences related to factorial numbers

Cf. A006882, A063170, A263529, A295099, A295100.

Table[n! SeriesCoefficient[Exp[n x] (1 + Exp[x^2/2] x (1 + Sqrt[Pi/2] Erf[x/Sqrt[2]])), {x, 0, n}], {n, 0, 20}]

a(n) ~ c * n^n, where c = 1 + exp(1/2) * (1 + sqrt(Pi/2) * erf(1/sqrt(2))) = 4.0594074053425761445394754992332... - Vaclav Kotesovec, Aug 21 2018

A295100 a(n) = n! * [x^n] exp(nx)/(1 - 2x).

Original entry on oeis.org

1, 3, 20, 201, 2688, 44815, 894528, 20792205, 551518208, 16438822587, 543934387200, 19783668211153, 784536321392640, 33689132092480839, 1557397919735103488, 77117362592836807125, 4072280214605427376128, 228441851811771488284915, 13566762607790788699226112, 850372121882700252639269337

Offset: 0

Ilya Gutkovskiy, Nov 14 2017

nonn

The n-th term of the n-th binomial transform of A000165.

Robert Israel, Table of n, a(n) for n = 0..375
N. J. A. Sloane, Transforms
Index entries for sequences related to factorial numbers

Cf. A000165, A010844, A063170, A082032, A295098, A295099.

S:= series(exp(n*x)/(1-2*x),x,51):
seq(n!*coeff(S,x,n),n=0..50); # Robert Israel, Nov 14 2017

Table[n! SeriesCoefficient[Exp[n x]/(1 - 2 x), {x, 0, n}], {n, 0, 19}]

a(n) ~ 2^n * exp(n/2) * n!. - Vaclav Kotesovec, Nov 14 2017

a(n) = n! * Sum_{k=0..n} n^k*2^(n-k)/k! = 2^n*Gamma(n+1, n/2)*exp(n/2). - Robert Israel, Nov 14 2017

cp's OEIS Frontend

A295098 a(n) = n! * [x^n] exp(nx)(1 + exp(x^2/2)x(1 + sqrt(Pi/2)*erf(x/sqrt(2)))).

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A295100 a(n) = n! * [x^n] exp(nx)/(1 - 2x).

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cp's OEIS Frontend

A295098 a(n) = n! * [x^n] exp(n*x)*(1 + exp(x^2/2)*x*(1 + sqrt(Pi/2)*erf(x/sqrt(2)))).

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Author

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Mathematica

Formula

A295100 a(n) = n! * [x^n] exp(n*x)/(1 - 2*x).

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Author

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Programs

Maple

Mathematica

Formula

A295098 a(n) = n! * [x^n] exp(nx)(1 + exp(x^2/2)x(1 + sqrt(Pi/2)*erf(x/sqrt(2)))).

A295100 a(n) = n! * [x^n] exp(nx)/(1 - 2x).