A338377 -id:A338377 - cp's OEIS frontend

A238223 Decimal expansion of a constant related to A088716.

2, 1, 7, 9, 5, 0, 7, 8, 9, 4, 4, 7, 1, 5, 1, 0, 6, 5, 4, 9, 2, 8, 2, 2, 8, 2, 2, 4, 4, 2, 3, 1, 9, 8, 2, 0, 8, 8, 6, 6, 0, 4, 5, 3, 9, 5, 6, 2, 9, 3, 9, 9, 6, 3, 4, 8, 1, 2, 3, 4, 0, 1, 7, 6, 2, 6, 5, 8, 7, 3, 3, 6, 2, 9, 2, 5, 3, 7, 0, 9, 4, 4, 9, 1, 2, 5, 9, 6, 3, 2, 2, 9, 8, 6, 2, 2, 9, 4, 5, 1, 4, 4, 8, 8, 9, 0

Offset: 0

Vaclav Kotesovec, Feb 21 2014

			0.21795078944715106549282282244231982088...

Michael Borinsky, Gerald V. Dunne, and Karen Yeats, Tree-tubings and the combinatorics of resurgent Dyson-Schwinger equations, arXiv:2408.15883 [math-ph], 2024. See p. 13.

Cf. A088716, A088715, A158884, A159606, A182962, A193332, A156326, A338377.

Equals lim n->infinity A088716(n)/(n!*n^2).

A113668 Self-convolution 8th power of A113674, where a(n) = A113674(n+1)/(n+1).

Original entry on oeis.org

1, 8, 156, 4696, 186406, 9053640, 515875660, 33585910968, 2453913830097, 198609146859416, 17630476159933080, 1703025192274201272, 177846105338917975896, 19968484152350242447288

Offset: 0

Paul D. Hanna, Nov 04 2005

nonn

From Vaclav Kotesovec, Oct 23 2020: (Start)
In general, for k>=1, if g.f. satisfies: A(x) = (1 + x*d/dx[x*A(x)] )^k, then a(n) ~ c(k) * k^n * n! * n^((k-1)/k), where c(k) is a constant (dependent only on k).
c(k) tends to A238223*exp(1) = 0.592451670452494179138706... if k tends to infinity.
(End)

Vaclav Kotesovec, Table of n, a(n) for n = 0..330

Cf. A113674, A113662, A113663, A113664, A113665, A113666, A113667, A338377.

{a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^8);polcoeff(A,n,x)}

G.f. satisfies: A(x) = (1 + x*d/dx[x*A(x)] )^8.

a(n) ~ c * 8^n * n! * n^(7/8), where c = 0.6523348263871879460325... - Vaclav Kotesovec, Oct 23 2020

cp's OEIS Frontend

A238223 Decimal expansion of a constant related to A088716.

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