A377741 -id:A377741 - cp's OEIS frontend

A377828 E.g.f. satisfies A(x) = (1 + x)^3 * exp(x * A(x)).

1, 4, 21, 193, 2669, 48711, 1113325, 30615019, 984983193, 36319515355, 1510538562641, 69968975169567, 3572684914283941, 199389519518767111, 12075888110164192917, 788850329621989132771, 55289606764547108653361, 4138807268239824817387443, 329564746571982961088975257

Offset: 0

Seiichi Manyama, Nov 09 2024

nonn

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

Cf. A377826, A377827.

Cf. A377741, A377811.

a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(3*k+3, n-k)/k!);

E.g.f.: (1+x)^3 * exp( -LambertW(-x*(1+x)^3) ).
E.g.f.: -LambertW(-x*(1+x)^3)/x.
a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(3*k+3,n-k)/k!.

A377740 E.g.f. satisfies A(x) = exp(x) * (1 + x * A(x))^2.

Original entry on oeis.org

1, 3, 19, 199, 2957, 57341, 1377175, 39531927, 1321803705, 50491876825, 2170432191491, 103726081148339, 5456983990544773, 313449393386822421, 19521567325327386831, 1310428405901227674511, 94325931842372734994417, 7248016420075574268626225, 592190617414334419733622139

Offset: 0

Seiichi Manyama, Nov 05 2024

nonn

Cf. A072597, A377741.

Cf. A295238, A377574.

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

E.g.f.: 4*exp(x)/(1 + sqrt(1 - 4*x*exp(x)))^2.
a(n) = n! * Sum_{k=0..n} (k+1)^(n-k-1) * binomial(2*k+2,k)/(n-k)!.
a(n) = A295238(n+1)/(n+1).

cp's OEIS Frontend

A377828 E.g.f. satisfies A(x) = (1 + x)^3 * exp(x * A(x)).

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