A377580 -id:A377580 - cp's OEIS frontend

A377579 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^4.

1, 4, 20, 204, 3112, 61220, 1523064, 45456292, 1586426720, 63461164932, 2862300600040, 143766016251044, 7959047336014416, 481550056915454020, 31615435540393172888, 2238661916541220434660, 170070509857455107126464, 13798559748847266924993284, 1190848786811966457102586824

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A161632, A377578.

Cf. A377580, A377581.

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

E.g.f.: B(x)^4, where B(x) is the e.g.f. of A377581.

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

A377581 E.g.f. satisfies A(x) = 1 + x * exp(x*A(x)^4).

Original entry on oeis.org

1, 1, 2, 27, 340, 6485, 156486, 4532647, 155359016, 6116223465, 272369488330, 13537882005131, 742838308204092, 44605728508797469, 2909444391161677838, 204844046364505460655, 15484082153045052133456, 1250714994867101307618257, 107511883999692161772696210

Offset: 0

Seiichi Manyama, Nov 02 2024

nonn

Cf. A161631, A364978, A364979.

Cf. A377579, A377580.

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

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

cp's OEIS Frontend

A377579 E.g.f. satisfies A(x) = (1 + x * exp(x*A(x)))^4.

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