A361092 -id:A361092

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A361090

E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)) ).

+10
4

1, 1, 3, 7, -11, -239, -179, 24991, 192025, -3955391, -89483399, 552615031, 46231717621, 254468241457, -26683006147979, -571848064714289, 14926049610344881, 825004339886219521, -2973711136010539535, -1134313888244827421465, -17734152216328857754739

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Winston de Greef, Table of n, a(n) for n = 0..399

FORMULA

a(n) = n! * Sum_{k=1..n} (-n+k+1)^(k-1) * binomial(n-1,n-k)/k! for n>0.

PROG

(PARI) a(n) = if(n==0, 1, n!*sum(k=1, n, (-n+k+1)^(k-1)*binomial(n-1, n-k)/k!));

CROSSREFS

Cf. A161630, A212722, A212917, A361091, A361092.

Cf. A361067, A361095.

KEYWORD

sign

AUTHOR

Seiichi Manyama, Mar 01 2023

STATUS

approved

A361091

E.g.f. satisfies A(x) = exp( x/(1 - x/A(x)^2) ).

+10
4

1, 1, 3, 1, -71, -19, 10051, 12349, -3185391, -9346247, 1797304771, 9717361721, -1582301193527, -13722004186331, 2000705907453891, 25552516703201461, -3432004488804778079, -60960914621687232271, 7660860906885122096515

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Winston de Greef, Table of n, a(n) for n = 0..380

FORMULA

a(n) = n! * Sum_{k=0..n} (-2*n+2*k+1)^(k-1) * binomial(n-1,n-k)/k!.

PROG

(PARI) a(n) = n!*sum(k=0, n, (-2*n+2*k+1)^(k-1)*binomial(n-1, n-k)/k!);

CROSSREFS

Cf. A161630, A212722, A212917, A361090, A361092.

Cf. A361068, A361096.

KEYWORD

sign

AUTHOR

Seiichi Manyama, Mar 01 2023

STATUS

approved

A365037

E.g.f. satisfies A(x) = exp(x * (1 + x/A(x)^3)).

+10
2

1, 1, 3, -11, -11, 1341, -14339, -168923, 8905065, -85313735, -4604578919, 197455645641, -273728455571, -267002430142187, 9427821270512373, 178475402982086701, -28273343910563670959, 713736314833387866225, 51907546734507018043057

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Lambert W-Function.

FORMULA

E.g.f.: exp( x + LambertW(3*x^2*exp(-3*x))/3 ).

a(n) = n! * Sum_{k=0..n} (-3*n+3*k+1)^(k-1) * binomial(k,n-k)/k!.

PROG

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(3*x^2*exp(-3*x))/3)))

CROSSREFS

Cf. A125500, A143768, A363354, A363529, A365035, A365036.

Cf. A361092.

KEYWORD

sign

AUTHOR

Seiichi Manyama, Aug 17 2023

STATUS

approved

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