A295098 -id:A295098 - cp's OEIS frontend

A295099 a(n) = n! * [x^n] exp(nx)/sqrt(1 - 2x).

1, 2, 11, 96, 1145, 17320, 317547, 6843872, 169603793, 4752704160, 148631984075, 5132717953792, 194022218612169, 7969667589513344, 353510496652374635, 16842274069331520000, 857827370723082312737, 46516913938434654949888, 2675772791433589181094027, 162742831545094476694814720

Offset: 0

Ilya Gutkovskiy, Nov 14 2017

nonn

The n-th term of the n-th binomial transform of A001147.

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. A001147, A063170, A081367, A084262, A295098, A295100.

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

a(n) ~ 2^(n+1) * n^n / exp(n/2). - Vaclav Kotesovec, Nov 14 2017

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

A295099 a(n) = n! * [x^n] exp(nx)/sqrt(1 - 2x).

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

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cp's OEIS Frontend

A295099 a(n) = n! * [x^n] exp(n*x)/sqrt(1 - 2*x).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A295099 a(n) = n! * [x^n] exp(nx)/sqrt(1 - 2x).

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