A335537 - OEIS

A335537

a(n) = n! [x^n] exp(2*x)*(y*sinh(x*y) + cosh(x*y)) and y = sqrt(x).

1, 2, 6, 23, 88, 332, 1294, 5252, 21872, 92888, 402784, 1782288, 8028904, 36768656, 171054160, 807703688, 3867540736, 18765870208, 92212515136, 458609391488, 2307237770496, 11736266317952, 60334416641536, 313342967240960, 1643352523119232, 8700550165605632

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) ~ 3^(2*n/3 - 5/6) * exp(32/81 - 8*(2*n/3)^(1/3)/9 + 2*(2*n/3)^(2/3) - n/3) * n^((n+1)/3) / (2^(2*n/3 + 1/6)). - Vaclav Kotesovec, Jun 24 2020

MAPLE

aList := proc(len) local H; H := (x, y) -> exp(2*x)*(y*sinh(x*y) + cosh(x*y)):

series(H(x, sqrt(x)), x, len+1): seq(k!*coeff(%, x, k), k=0..len-1) end:

aList(30);

CROSSREFS