A377574 -id:A377574 - cp's OEIS frontend

A377575 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^3.

1, 3, 30, 483, 11100, 334035, 12478698, 558058179, 29104042152, 1735547479587, 116539815603630, 8704631976941043, 716019297815418732, 64326542671867079955, 6267631435921525638738, 658359915933162131600355, 74168964857766293453918928, 8921104769819780822122624323

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A006153, A377574, A377576.

Cf. A364983, A377554.

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

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A364983.

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

A377576 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^4.

Original entry on oeis.org

1, 4, 52, 1116, 34408, 1394340, 70298424, 4248802516, 299752943200, 24196951718532, 2200519882434280, 222683725755611604, 24824104612186789584, 3023063956714780554628, 399343825987950226379416, 56879649386095684434783060, 8689968793295620150120679104

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A006153, A377574, A377575.

Cf. A364987, A377577.

a(n) = n!*sum(k=0, n, k^(n-k)*binomial(4*k+4, k)/((k+1)*(n-k)!));

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A364987.

a(n) = n! * Sum_{k=0..n} k^(n-k) * binomial(4*k+4,k)/( (k+1)*(n-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

A377575 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^3.

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A377576 E.g.f. satisfies A(x) = (1 + x * exp(x) * A(x))^4.

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

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