A377583 Expansion of e.g.f. (1 + x * exp(x))^4.

1, 4, 20, 108, 616, 3620, 21624, 129892, 778208, 4621572, 27080680, 156080804, 883304976, 4905620356, 26743018904, 143219056740, 754280089024, 3911369843204, 19995029207496, 100885122939172, 502952669726960, 2480084192804484, 12107351426245240, 58565261434872548

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

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

G.f.: (1 - 36*x + 595*x^2 - 5970*x^3 + 40543*x^4 - 196752*x^5 + 702365*x^6 - 1871250*x^7 + 3740456*x^8 - 5614440*x^9 + 6362360*x^10 - 5588880*x^11 + 3979680*x^12 - 2196672*x^13 + 663552*x^14) / ((1-x)^2*(1-2*x)^3*(1-3*x)^4*(1-4*x)^5).

Prog

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

Crossrefs

Cf. A002999, A377582.

Cf. A377399, A377576.

Sequence in context: A321111 A319321 A321574 * A225621 A375303 A020084

Adjacent sequences: A377580 A377581 A377582 * A377584 A377585 A377586

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 02 2024

Status

approved