A381206 Expansion of e.g.f. 1/(1 - x*cosh(x))^2.

1, 2, 6, 30, 192, 1450, 12960, 133574, 1550976, 20055186, 285903360, 4452231982, 75186726912, 1368588922298, 26709799753728, 556339845854550, 12318065768693760, 288894650033594914, 7154212267816648704, 186545064693433665854, 5108590743587243950080

Offset

0,2

Comments

As stated in the comment of A185951, A185951(n,0) = 0^n.

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{k=0..n} (k+1)! * A185951(n,k).

Prog

(PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
a(n) = sum(k=0, n, (k+1)!*a185951(n, k));

Crossrefs

Cf. A205571, A381207.

Cf. A185951.

Sequence in context: A353982 A340243 A373659 * A375810 A375806 A078700

Adjacent sequences: A381203 A381204 A381205 * A381207 A381208 A381209

Keyword

nonn,new

Author

Seiichi Manyama, Feb 17 2025

Status

approved